WASHINGTON — With his hold on the Senate in increasing jeopardy, Senator Mitch McConnell, Republican of Kentucky and the majority leader, sought to rally his forces this week by rekindling a rivalry with a familiar foe: Barack Obama.

In a highly partisan, no-holds barred online interview with Lara Trump, President Trump’s daughter-in-law and campaign adviser, Mr. McConnell declared on Monday that the former president “should have kept his mouth shut,” rather than have the temerity to excoriate the Trump administration’s pandemic response. He omitted the fact that Mr. Obama made the comments, in which he described Mr. Trump’s handling of the crisis as “an absolute chaotic disaster,” in a private call with alumni of his administration that was leaked.

“I think it is a little bit classless, frankly, to criticize an administration that comes after you,” Mr. McConnell said on a day when Mr. Trump repeatedly attacked Mr. Obama on Twitter, suggested in a Rose Garden news conference that the former president was a criminal, and called his predecessor’s tenure “the most corrupt administration in U.S. history!”

“You had your shot — you were there for eight years,” Mr. McConnell added derisively, referring to Mr. Obama, who for years has remained notably quiet about Mr. Trump’s performance, much to the chagrin of many Democrats who wish he would vocally denounce his successor.

Like Mr. Trump, Mr. McConnell aggressively sought to shift responsibility for the pandemic and the resulting national upheaval to both China and the Obama administration, which Mr. McConnell said had not left behind “any kind of game plan” for dealing with such an outbreak.

That assertion drew ridicule from veterans and allies of the Obama administration who quickly noted that the previous administration had drawn up a National Security Council document titled “Playbook for Early Response to High-Consequence Emerging Infectious Disease Threats and Biological Incidents,” which included the potential for a novel coronavirus outbreak.

“We literally left them a 69-page Pandemic Playbook…. that they ignored,” Ron Klain, who coordinated the Obama administration’s Ebola response, said on Twitter.

Mr. McConnell has never held back his disdain for the Democratic president he sought to obstruct at nearly every turn over eight years, and the feeling was decidedly mutual. Theirs was a particularly dysfunctional policy and personal relationship, though the unvarnished animosity between Mr. Trump and Speaker Nancy Pelosi may exceed it.

Remember Mr. Obama’s stinging comeback to those urging that he socialize more with congressional Republicans to try to forge a warmer rapport? “Why don’t you have a drink with Mitch McConnell!” he cracked in 2013 at the White House Correspondents’ Dinner, to much laughter and applause. He softened that tone when Republicans gained control of the Senate in 2014, and expressed an appreciation for Kentucky bourbon.

But no real engagement ever materialized as the Republicans, led by Mr. McConnell, fought tooth and nail on immigration, health care, the environment and gun safety, capping off a rancorous time with Mr. McConnell’s unilateral decision in early 2016 to block Mr. Obama’s nominee to the Supreme Court.

Mr. McConnell saw Mr. Obama as an amateur catapulted to the highest office in the land after a brief swing through the Senate. He chafed under what he deplored as professorial lectures by Mr. Obama during his sessions with congressional leaders. In his memoir, Mr. McConnell recounted watching a full inning of televised baseball while the president went on nonstop about a subject by telephone.

During his appearance on the online program that delivers an exceedingly Trump-centric view of the world, Mr. McConnell said he believed that Mr. Obama should be more deferential to his successor, as their Republican presidential predecessors had been to Bill Clinton and Mr. Obama.

“I remember President George W. Bush and his father went through eight years of Democratic administrations after they left office and kept their mouths shut because they didn’t feel it was appropriate for presidents to criticize even presidents of another party,” Mr. McConnell said.

Mr. Obama’s office did not issue a response to Mr. McConnell’s statements. But one person with knowledge of the president’s thinking, speaking on the condition of anonymity, said that Mr. McConnell’s reference to past presidential norms was particularly outrageous given Mr. Trump’s norm-breaking attacks on his predecessor.

The Obama camp viewed Mr. McConnell’s comments as a weak effort to dissuade Mr. Obama, who remains very popular, from weighing in on the presidential campaign. The tactic will fail miserably, they said, noting that Mr. Obama’s comments to his former staff members last Friday showed that he intended to be all-in for his former vice president, Joseph R. Biden Jr.

Mr. McConnell has drawn pushback for his remarks to conservative commentators in recent weeks. His suggestion that financially strapped states file for bankruptcy rather than count on a federal bailout was condemned by members of both parties. On Tuesday, Senator Chuck Schumer of New York, the Democratic leader, blasted Mr. McConnell for his remark on Monday that Senate Republicans have not yet “felt the urgency” to immediately move ahead with the next phase of pandemic relief legislation.

“We live in a divided nation, but one thing that pretty much everyone agrees on is there is a great deal of urgency right now, Leader McConnell,” Mr. Schumer said on the Senate floor.

Senate Republicans are facing a more difficult election cycle than anticipated, with the coronavirus outbreak unsettling the November outlook by putting some Republican incumbents behind their challengers and leaving others in real peril, giving Democrats more opportunity to assume the majority.

In his Monday interview, Mr. McConnell revealed glimmers of his own game plan for 2020 as he strives to get re-elected himself: Don’t emphasize what Republicans have done, but alarm voters about what Democrats have in store.

“What we need to do is to remind people of what the other guys will do if they take the government,” he told Ms. Trump. “If they take the government, they are going to change this country for the worse for a long, long time.”

Warning that Democrats would quickly try to undo the successful push he has made in tandem with Mr. Trump to fill federal court vacancies with conservatives, Mr. McConnell said he considered the coming contest to be “the single most important election in American history, because there are vast differences between the two sides.”

Given their competing interests and the stakes of the coming election for both, Mr. Obama and Mr. McConnell will almost certainly have much more to say about each other before Nov. 3.