WASHINGTON — The first time that Senator John Kennedy, Republican of Louisiana, went on a Sunday television talk show and suggested that it might have been Ukraine, rather than Russia, that interfered in the 2016 election, he drew so much criticism that he quickly apologized.

But the following week, Mr. Kennedy was back on the Sunday circuit, returning to a claim that contradicted the findings of American intelligence officials, who long ago concluded that Moscow attacked the election, and who recently told congressional officials that Russia had been engaged in a disinformation campaign to frame Ukraine for it.

And this week, as the Senate returned from its Thanksgiving recess facing the prospect of an impeachment trial in the new year, some other Republican senators have joined Mr. Kennedy in latching on to the theory, testing out a pivot as they attempt to mount a more vigorous defense of the president.

The issue is crucial to the impeachment story, because it mirrors a claim that Mr. Trump made — and asked President Volodymyr Zelensky of Ukraine to investigate — in a July phone call that sparked the inquiry. Democrats argue that the president’s bid to pressure Ukraine to announce that investigation, and another into former Vice President Joseph R. Biden Jr., was a dangerous abuse of power for his own political gain, and grounds for impeachment. Republicans are toiling to put the request in a more positive light.