WASHINGTON — Donald J. Trump’s lawyers laid out their first extended impeachment defense on Monday, arguing that holding him responsible for the deadly Jan. 6 Capitol attack was nothing more than “political theater” by Democrats, and that the Senate had no power to sit in judgment of a former president.

In a 78-page brief submitted to the Senate on the eve of the trial, the lawyers asserted that Mr. Trump did not “direct anyone to commit unlawful actions” or deserve blame for the conduct of what they called a “small group of criminals” who stormed into the Capitol. They said the former president’s rash of falsehoods about a stolen election, delivered at a rally outside the White House before the pro-Trump mob mounted its assault, were protected by the First Amendment.

Relying on contested legal arguments, they also contended that the Senate “lacks jurisdiction” to try a former president because, by definition, he cannot be removed.

Hours later, in their own filing, the Democratic impeachment managers from the House called the lawyers’ attempt to dismiss their charge “wholly without merit,” and argued that the Constitution gave them clear jurisdiction to proceed.

Mr. Trump’s defense appeared to be aimed at persuading at least 34 Republicans needed to win acquittal on the charge of “incitement of insurrection” to stick with the former president, despite their outrage over an assault that put their lives at risk. And it brimmed with partisan attacks.

“This impeachment proceeding was never about seeking justice,” wrote the lawyers, Bruce L. Castor Jr., David I. Schoen and Michael T. van der Veen. “Instead, this was only ever a selfish attempt by Democratic leadership in the House to prey upon the feelings of horror and confusion that fell upon all Americans across the entire political spectrum upon seeing the destruction at the Capitol on Jan. 6 by a few hundred people.”

The House managers framed it instead as an effort to hold Mr. Trump accountable for egregious actions and to disqualify him from holding office in the future.

“As charged in the article of impeachment, President Trump violated his oath of office and betrayed the American people,” the managers wrote. “His incitement of insurrection against the United States government — which disrupted the peaceful transfer of power — is the most grievous constitutional crime ever committed by a president.”

The flurry of written arguments arrived as the rules and timeline for the trial came into sharper focus on Monday and as Washington braced for the second impeachment trial of Mr. Trump in two years. Top Senate leaders reached a bipartisan agreement to set up an exceptionally swift proceeding that could conclude in less than half of the time of Mr. Trump’s first trial.

The rules allow each side up to 16 hours to make its case and give the House managers the option of forcing a debate and vote on whether to include witnesses at the trial. Senators had originally planned to honor a request from Mr. Schoen to recess the trial at sundown on Friday and reconvene on Sunday to observe the Jewish Sabbath, but he abruptly pulled back his request late Monday, saying the defense could go ahead without him.

Either way, a final vote on conviction or acquittal could take place early next week.

After beginning Mr. Trump’s first impeachment trial in utter acrimony last year, Senators Chuck Schumer, Democrat of New York and the majority leader, and Mitch McConnell of Kentucky, the Republican leader, both lauded the agreement on Monday as fair, as did Mr. Trump’s team, setting a more cooperative tone for the proceeding that senators hope will lend legitimacy to its outcome.

“It preserves due process and the rights of both sides,” Mr. McConnell said. “It will give senators, as jurors, ample time to review the case and the arguments that each side will present.”

Republican leaders worry that days of intense focus on a graphic retelling of the former president’s campaign to overturn his election loss could further cleave their party and distract from efforts to turn the page on Mr. Trump. Already, a half-dozen Republican senators have indicated they are open to conviction, but others are warily eyeing an intense backlash against the 10 House Republicans who voted to impeach.

The House managers planned to argue that as president, Mr. Trump sowed the lie that he won the 2020 election, pressured election officials to overturn the results and finally trained his attention on Congress, summoning and directing a mob of supporters to try to stop lawmakers meeting at the Capitol on Jan. 6 from formalizing President-elect Joseph R. Biden Jr.’s victory.

For Democrats now in control of Congress and the White House, the proceeding threatens to complicate Mr. Biden’s attempts to quickly pass a nearly $2 trillion coronavirus stimulus bill. Senators have vowed to continue working on the plan before the trial begins each day, but if nothing else, the trial will prove an unwelcome distraction for a White House trying to show it is focused on a once-in-a-century health crisis.

“I’m just not going to have any more for you, weighing in on impeachment,” Jen Psaki, the White House press secretary, told reporters on Monday. “It’s a big story. But our focus is on the ‘American Rescue Plan.’”

Perhaps fittingly for a trial without precedent, the proceeding is to begin on Tuesday with a lengthy debate over whether it is even constitutional for the Senate to go forward. Mr. Trump’s lawyers and the House managers will be given up to four hours to debate the point before senators take an up-or-down vote on whether to proceed.

A majority of senators have already indicated they believe trying Mr. Trump is constitutional, but how many Republicans vote to advance could be instructive. Late last month, 45 of them voted to effectively dismiss the case on constitutional grounds. But since then, a prominent Republican lawyer, Charles J. Cooper, has joined those arguing against their position, and several senators have said they might reconsider.

The Constitution does not explicitly say one way or another whether a former official can be impeached or tried for offenses committed while in office.

Analyzing the plain text and citing a 1787 debate over the Constitution, Mr. Trump’s team argued on Monday that the founders intended impeachment as a mechanism only to remove someone from office. Because Mr. Trump is now a private citizen, they wrote, the House’s charge is “moot and a non-justiciable” and removing him would be “patently ridiculous.”

A majority of constitutional scholars disagree with that reasoning. They say the founders never intended to exempt someone like Mr. Trump from trial and point out that the Senate voted in the 19th century to try a former war secretary.

In their brief, the House managers indicated they would make a similar argument.

“Presidents swear a sacred oath that binds them from their first day in office through their very last,” they wrote. “There is no ‘January exception’ to the Constitution that allows presidents to abuse power in their final days without accountability.”

The managers also pre-emptively attacked as “utterly baseless” claims by Mr. Trump’s lawyers that he could not be held accountable for his remarks around the riot because they were protected by the First Amendment.

And they were just as blunt about Mr. Trump’s more substantive defenses: “To call these responses implausible would be an act of charity,” they wrote.

But in its brief on Monday, Mr. Trump’s legal team was adamant that it was the prosecution substituting opinions about what happened with facts.

The lawyers said that when Mr. Trump repeatedly urged thousands of supporters gathered outside the White House on the morning of the attack to “fight like hell,” he meant it in a “figurative sense.” The filing dedicates a section to the use of the word “fight” by Democrats, including Speaker Nancy Pelosi, and says that Mr. Trump should be taken at his word when he also told the crowd to proceed “peacefully.”

The lawyers also argued that evidence showing some rioters had planned their attack in advance exonerated Mr. Trump. But that fact alone does not undermine the House’s charge, which says the incitement took place over a matter of weeks as Mr. Trump whipped up supporters to “stop the steal” — not just on Jan. 6.

“The real truth is that the people who criminally breached the Capitol did so of their own accord and for their own reasons, and they are being criminally prosecuted,” Mr. Trump’s lawyers wrote.

At another point, despite knocking the House managers for relying on journalistic accounts, the lawyers cited the right-wing Gateway Pundit blog to assert — contrary to evidence — that there had been some “anti-Trump” elements among the rioters.

Foreshadowing what may be one of the most contentious factual disputes of the trial, the defense team wrote in a footnote the House’s damning charge that Mr. Trump “delighted” in watching the attack and purposefully refrained from sending in reinforcements was “absolutely wrong.”

His lawyers said Mr. Trump and the White House “took immediate steps” to “provide whatever was necessary to counteract the rioters.” Any delay was the result of “complex procedural elements involved in quelling a riot at the Capitol and on the Mall.”

“There is no legitimate proof, nor can there ever be, that President Trump was ‘delighted’ by the events at the Capitol,” they wrote. “He, like the rest of the country, was horrified at the violence.”

The House managers who are prosecuting the case disagreed, but their evidentiary record is thin in this area. They based their contention on news reports and accounts by lawmakers who called Mr. Trump’s aides pleading for help that day, but also on Mr. Trump’s own words. In particular, the prosecutors noted that even as the rampage was unfolding, Mr. Trump was still targeting Vice President Mike Pence on Twitter for not unilaterally overturning the result as he oversaw the counting of electoral votes.

Charlie Savage contributed reporting from Washington, and Maggie Haberman from New York.