Former President Donald J. Trump’s lawyers denied on Tuesday that he incited the deadly assault on the Capitol and argued that the Senate had no power to try a former president, as House prosecutors made their case that Mr. Trump was “singularly responsible” for the Jan. 6 rampage and must be convicted and barred from holding any future office.

The dueling filings provided the clearest preview yet of a politically fraught impeachment trial — the second in just a year — scheduled to begin in earnest next Tuesday. Both sides indicated they were ready for a debate over the constitutionality of trying a former president. They were also lining up diametrically opposed interpretations of a set of events witnessed on live television across the nation.

In his first formal answer to the “incitement of insurrection” charge against him, Mr. Trump’s lawyers denied that he was responsible for the Capitol riot or that he intended to interfere with Congress’s formalizing of President Biden’s election win. They said his words to supporters, some who later stormed the building — “if you don’t fight like hell, you’re not going to have a country anymore” — were protected by his First Amendment right of free speech. They said they were not meant as a reference to violent action, but “about the need to fight for election security in general.”

“It is denied that President Trump incited the crowd to engage in destructive behavior,” the lawyers, Bruce L. Castor Jr. and David Schoen, wrote in the 14-page filing.

Notably, the document avoided repeating or attempting to defend Mr. Trump’s bogus claims that the November election had been “stolen” from him by widespread fraud, which the former president had wanted to be the central feature of his defense. But his lawyers in effect argued that Mr. Trump believed he won, and therefore was within his rights to “express his belief that the election results were suspect.” His claims could not be disproved, they added, because there was “insufficient evidence.” (Judges rejected more than 60 lawsuits by Mr. Trump and his allies claiming varying degrees of fraud or irregularities.)

Above all, the former president’s lawyers said the Constitution did not permit the Senate to try a former president after he had left office — despite the fact that the Senate has tried a former official in the past.

The response arrived two hours after the nine House Democrats preparing to prosecute the case argued in their own 80-page pretrial brief that Mr. Trump was directly to blame for the violent attack on Jan. 6 and a broader attack on democracy that showed he would do anything to “reassert his grip on power” if he were allowed to seek election again.

“President Trump has demonstrated beyond doubt that he will resort to any method to maintain or reassert his grip on power,” wrote the managers, led by Representative Jamie Raskin of Maryland. “A president who violently attacks the democratic process has no right to participate in it.”

The House prosecutors also refuted Mr. Trump’s constitutional challenge to the case, asserting that history and even conservative constitutional theory supported the Senate’s right to try a former president.

“There is no ‘January exception’ to impeachment or any other provision of the Constitution,” the managers wrote. “A president must answer comprehensively for his conduct in office from his first day in office through his last.”

They likewise insisted that Mr. Trump’s First Amendment right to free speech did not shield him from responsibility for inciting violence that would seek to do harm to the Constitution, undermining all the rights enshrined there, including free speech.

Mr. Trump’s response took an unusual form, addressing the House’s article of impeachment point by point. It also appeared to be somewhat hastily assembled after Mr. Trump shook up his legal team just 48 hours before the brief was due; the response was addressed to the “Unites States Senate.”