WASHINGTON — Senator Mitch McConnell, the majority leader, insisted on Wednesday that Speaker Nancy Pelosi accept his terms for President Trump’s impeachment trial and promptly deliver the charges from the House, as a growing number of Senate Democrats signaled that they, too, were eager to begin the proceeding.
A day after he announced that he had the votes to conduct a trial without agreeing to Democrats’ demands for witnesses, Mr. McConnell said that the House had no choice now but to end “shameless game-playing” and transmit the two articles of impeachment against Mr. Trump that it approved last month.
“There will be no haggling with the House over Senate procedure,” Mr. McConnell, a Kentucky Republican, said on the Senate floor. “We will not cede our authority to try this impeachment. The House’s turn is over. The Senate has made its decision.”
Though they voiced deference to the speaker, a growing number of Senate Democrats said on Wednesday that they were losing patience with the delay and wanted the trial to begin.
“It’s pretty clear there is not going to be any agreement,” said Senator Doug Jones of Alabama, the most politically vulnerable Democratic incumbent. “The rules are going to be what they are, and she should know that now, so let’s just go ahead.”
Liberals and senior lawmakers joined the call as well.
“I don’t see what good delay does,” said Senator Dianne Feinstein, the senior senator from Ms. Pelosi’s home state, California.
Their impatience fueled a growing sense in both chambers that three weeks after the House voted to impeach Mr. Trump, Ms. Pelosi may soon act to start the trial.
Ms. Pelosi has been withholding the charges in an unusual bid to help Democrats press their case that any fair trial must include the guarantee of new witnesses and documents. On Tuesday evening, she demanded that Mr. McConnell make public his proposed rules for the proceeding before she delivered the articles so that Democrats could “see the arena in which we will be participating.”
But Mr. McConnell appeared in no rush to do so. Citing the heightened tensions in the Middle East — where Iran fired missiles at United States forces early Wednesday in Iraq — the Senate leader charged that the speaker was playing a dangerous game on impeachment at the worst possible time.
“At the very same time a global crisis was unfolding in real time, she published another ‘dear colleague’ letter saying she intends to keep our commander in chief in this limbo indefinitely,” Mr. McConnell said.
The pointed remarks were the latest in an escalating confrontation between two of the most powerful leaders Congress has seen in a generation.
Mr. McConnell, 78, and Ms. Pelosi, 79, each of whom has served for more than three decades, are considered master tacticians in their parties, and neither is known for backing down from a contentious fight. Both have a keen understanding of the political dynamics in their rank and file, and excel at consolidating their colleagues around a single position and refusing to budge.
Mr. McConnell’s objective in the current battle is to bring about a speedy acquittal of the president, belittling the House’s case in the process.
Ms. Pelosi, having carefully orchestrated the impeachment vote in the House, does not want to allow the Senate to quickly bury the matter without delving into additional witness accounts or documents. And if she cannot force Mr. McConnell to agree to those terms, she is determined at least to convince the public that the Senate trial is illegitimate — and, by extension, that Mr. Trump’s acquittal was rigged from the start.
The two leaders, whose relationship has grown chillier in recent years, have not spoken directly about impeachment stalemate, instead carrying out their terse exchanges in speeches and through the news media.
The latest comments from Mr. McConnell came in response to a letter from Ms. Pelosi to House colleagues late Tuesday in which she accused him of putting his loyalty to the president above the Constitution. In recent weeks, she has also referred to Mr. McConnell as “rogue” and complicit in a cover-up of what she described as the president’s misbehavior.
“This process is not only unfair but designed to deprive senators and the American people of crucial documents and testimony,” she wrote.
She said she needed details about what a trial would look like so she could choose the team that will prosecute the House’s case that Mr. Trump abused his power and then obstructed Congress. The charges stem from a House inquiry that concluded Mr. Trump pressured Ukraine to investigating his political rivals in a bid to bolster his re-election campaign, and then sought to conceal his actions from legislative oversight.
While Ms. Pelosi is widely expected to pick Representative Adam B. Schiff of California, the Intelligence Committee chairman who oversaw the House’s Ukraine inquiry, to lead the team of managers, she is still weighing the size and makeup of the rest of the team.
On Wednesday, Mr. McConnell reiterated that he intended to closely follow the model of President Bill Clinton’s 1999 impeachment trial, delaying any consideration of additional witnesses or evidence not included in the House inquiry until opening arguments are complete and senators have a chance to question the prosecution and defense.
In 1999, those procedures garnered unanimous support from senators, but Democrats this time are expected to oppose them en masse. The facts of the cases are simply different, they argue. Then, every witness of consequence had been questioned and their testimony made public before the trial began. Mr. Trump, on the other hand, succeeded in the fall in blocking the testimony of a dozen top officials and did not produce a single document to investigators.
At least three Senate Republicans have indicated they are open to potentially calling witnesses like John R. Bolton, the former national security adviser who said this week he would be willing to testify. But Democrats would have to find a fourth Republican willing to join with them to muster the majority needed to do so.
With Ms. Pelosi firmly backed by her own caucus, Mr. McConnell tried on Wednesday to drive a wedge between Democrats in the House and the Senate to increase pressure on the speaker.
He said Ms. Pelosi’s leverage to influence the Senate was “nonexistent” and urged Senator Chuck Schumer of New York, the Democratic leader, to listen to his own members who want the trial to begin quickly.
“He is a senior member of an independent branch of our bicameral legislature,” Mr. McConnell said of Mr. Schumer. “The Democratic leader does not need to continue to be in thrall to the speaker. He does not need to keep colluding with outside efforts to supplant the judgment of his own colleagues.”
Mr. Schumer, increasingly resigned to Mr. McConnell’s decision to blow past Democrats’ demands, offered the majority leader and Republican senators a warning in his own speech on the Senate floor. Mr. Schumer said he would force votes on calling witnesses and documents during the trial and the nation could judge at the ballot box the actions of each lawmaker.
“If the Senate rushes through the president’s impeachment, if we actually fail to try the case, as the Constitution demands, then the true acquittal the president craves will be unobtainable,” he said. “The American people will see right through a partisan trial and understand that a rush to judgment rendered that moot.”