A recording appears to capture Trump talking about Yovanovitch.

A lawyer representing Lev Parnas, an associate of Rudolph W. Giuliani, Mr. Trump’s personal lawyer, said on Friday that he turned over to congressional Democrats a recording that appeared to be of Mr. Trump speaking about Marie L. Yovanovitch, the United States ambassador to Ukraine at the time.

According to ABC News, which first reported the existence of the recording on Friday, Mr. Trump could be heard on the tape, saying, “Get rid of her.” The president went on to say: “Get her out tomorrow. I don’t care. Get her out tomorrow. Take her out. O.K.? Do it.”

Joseph A. Bondy, Mr. Parnas’s lawyer, described the recording as having “high materiality to the impeachment inquiry.” The emergence of the recording coincides with a push by Democrats in the Senate to call more witnesses and seek additional evidence for the trial.

Ms. Yovanovitch was removed from her post last spring on Mr. Trump’s orders after being the subject of a smear campaign by his allies, who saw her as an impediment to their agenda, which included efforts to force Ukraine to announce investigations into the Bidens.

The fight over admitting new evidence, like documents and witnesses, goes on.

Once Mr. Trump’s lawyers conclude their arguments, sometime between Saturday and Tuesday, senators are expected to have a short debate on whether to admit new evidence and witnesses to the trial. Republicans defeated an effort to consider the matter before the start of oral arguments, drawing outrage from Democrats, who have maintained that there could not be a fair trial without them.

The evidence-and-witnesses argument is the crux of the charge that Mr. Trump obstructed Congress. New evidence has emerged since the House completed its impeachment inquiry last year, and one of the president’s former national security advisers, John R. Bolton, said he would testify at the Senate trial if he received a subpoena. (Mr. Bolton did not testify before the House.)

This is an area where Democrats have been hoping to sway some of the Republicans who have signaled they might be open to hearing from witnesses, including Senators Susan Collins of Maine, Mitt Romney of Utah and Lisa Murkowski of Alaska. Democrats also are holding out hope for Senator Lamar Alexander of Tennessee, who is retiring at the end of this term.