Senator Mitch McConnell, Republican of Kentucky and the majority leader, was drafting trial rules that would not guarantee a vote to do so, rankling some conservatives but potentially sparing moderates a politically risky move. And in another bow to centrists who have insisted on it, Mr. McConnell was planning to allow votes on whether to call witnesses after opening arguments from both sides and questions by senators.

Senator Susan Collins, Republican of Maine, said Thursday that she would be inclined to vote in favor of new testimony at that point.

“While I need to hear the case argued and the questions answered, I tend to believe having additional information would be helpful,” she said in a statement. “It is likely that I would support a motion to call witnesses at that point in the trial, just as I did in 1999.”

The issue will be hotly debated when the trial resumes Tuesday, and the Senate is scheduled to vote on the rules for the proceeding.

Senator Chuck Schumer, the minority leader, said he would immediately call for a vote to subpoena witnesses and documents that could provide new information about Mr. Trump’s actions. Democrats have said the new evidence from Mr. Parnas proves that the Senate should press for documents that the administration refused to provide during the House investigation.

The evidence provided by Mr. Parnas adds significant detail to the public record about how the pressure campaign played out and new political peril for Mr. Trump as his lawyers seek to exonerate him. On Wednesday, Mr. Parnas told The New York Times that he believed the president knew about the efforts to dig up dirt on his political rivals.

Representative Val B. Demings, Democrat of Florida and one of the seven impeachment managers, tweeted Thursday that the assertions by Mr. Parnas confirmed that Mr. Giuliani and others were “working on the presidents orders.”