Senate Majority Leader Mitch McConnell, R-Ky., said Thursday that he has reached an “impasse” with Senate Minority Leader Chuck Schumer, D-N.Y., over moving forward with the rules governing a Senate trial of President Donald Trump, who was impeached by the House on Wednesday.

McConnell and Schumer have openly feuded in recent days over their competing views of what a Senate trial of Trump — who became just the third-ever president to be impeached — should look like.

House Democrats have said they may not submit the articles of impeachment to the Senate unless McConnell agrees to rules that ensure a fair trial, which Schumer has said should include witnesses who did not give testimony to the House. A continuing impasse could mean that Trump will have to wait indefinitely to be acquitted by the Republican-controlled Senate.

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In a brief Senate floor speech Thursday evening, McConnell said he’d had a “cordial” conversation with Schumer earlier in the day about the “potential paths forward” for a Senate trial.

He reiterated that he’d like the Senate to conform to the precedent set in 1999, during the Senate trial of then-President Bill Clinton, following his own impeachment. Back then, there was a two-resolution process: An initial agreement to first hear the prosecution and then the defense arguments, and a vote, later on, on whether to have witnesses or not.

Schumer has pushed for a single resolution that would set the parameters for the opening arguments and that would also allow for the calling of witnesses in the Senate trial of Trump. Schumer has said he wants the Senate, during its trial of Trump, to call as witnesses former national security adviser John Bolton and acting White House chief of staff Mick Mulvaney, as well as two others, to testify about Trump’s Ukraine dealings.

“We remain at an impasse, because my friend, the Democratic leader, continues to demand a new and different set of rules for President Trump,” McConnell said Thursday.

"He wants to break from the unanimous bipartisan precedent and force an all our nothing approach," McConnell added.

Bolton and Mulvaney did not testify during the House's impeachment inquiry.

McConnell said Schumer wanted "a special pretrial guarantee" that "House Democrats themselves did not bother to pursue as they assembled their case."

McConnell also criticized House Speaker Nancy Pelosi, D-Calif., for taking the “highly unusual step” of waiting to transmit the approved House articles of impeachment against Trump to the Senate.

McConnell said he didn’t understand the move by Pelosi and said, while cracking a smile, that he didn’t agree with the idea that delaying the transmission might give her leverage in dictating the rules of the Senate trial.

“I admit, I’m not sure what leverage there is from refraining from sending us something we do not want,” McConnell said. “But alas, if they can figure that out, they can explain it.”

Trump, meanwhile, tweeted Thursday night that he wanted "an immediate trial" and slammed Democrats for telling "the Senate how to run their trial."

So after the Democrats gave me no Due Process in the House, no lawyers, no witnesses, no nothing, they now want to tell the Senate how to run their trial. Actually, they have zero proof of anything, they will never even show up. They want out. I want an immediate trial! — Donald J. Trump (@realDonaldTrump) December 20, 2019

Pelosi, for her part, has also refrained from announcing her selection of House “managers” — or prosecutors — to present the case against Trump at the Senate trial. She said Wednesday night it would be “difficult to determine who the mangers would be” until “we see the area in which we will participating.”

The House, however, completed its last votes of the year earlier on Thursday. And McConnell said Thursday that Senators need not return to Washington for votes until Jan. 6, 2020. That may mean that the “impasse” could stretch into the new year, delaying the start of Trump’s Senate trial.

McConnell's speech was the latest salvo in ongoing skirmish between Republican and Democratic leaders in Congress, who have been going toe-to-toe amid the standoff over the next steps in Trump's impeachment.

Speaking to reporters, Pelosi — who would have to send the two House-passed articles of impeachment to the Senate before a trial of the president can begin — said she had no intention of taking action until she heard from McConnell about his plans.

Pelosi said she will move forward "when we see the process set forth in the Senate."

Earlier, McConnell said Pelosi "may be too afraid" to send the articles of impeachment to the Senate.

McConnell, speaking on the Senate floor earlier, also lambasted the impeachment as "the most rushed, least thorough, and most unfair ... in modern history." He said Pelosi "gave in to a temptation" and that the House impeached Trump "simply because they disagree with a presidential act."

Speaking with CNN, Rep. Jim Clyburn, D-S.C., one of the highest-ranking House Democrats, said delaying the articles was "necessary" because McConnell "made very clear he won't be fair" and that Democrats may hold onto the articles and not give them to the Senate for "as long as it takes" to ensure a fair trial.

"Until we can get some assurances from the majority leader that he is going to allow for a fair and impartial trial to take place, we would be crazy to walk in there knowing he set up a kangaroo court," he said.

The two articles of impeachment approved by the House on Wednesday charge Trump with abuse of power and obstruction of Congress.

Meanwhile, Democrats and Republicans on Thursday continued presenting their case for and against Trump's impeachment.

Democrats said if Trump is above accountability for his conduct outlined in the articles, impeachment will become meaningless. Republicans, meanwhile, said that if Trump can be impeached for that conduct, all future presidents are likely to be subjected to impeachments.

Hitting McConnell for remarks he made Thursday, Pelosi said she didn't suspect the Founding Fathers "suspected that we'd have a rogue leader in the Senate at the same time" as a rogue president.

McConnell said those articles are "fundamentally unlike any articles that any prior House of Representatives has ever passed" and the idea Democrats will withhold the articles suggests "House Democrats may be too afraid to even transmit their shoddy work product to the Senate."

"Looks like the prosecutors are getting cold feet in front of the entire country and second-guessing whether they even want to go to trial," McConnell said, trashing the "comical" idea that Democrats will now "sit on their hands."

Such actions "concede that their own allegations are unproven," McConnell said, suggesting that "every future president" could now face impeachment, "free to swamp the Senate with trial after trial, no matter how baseless."

"The framers built the Senate to provide stability," McConnell said, "to keep partisan passions from boiling over. The Senate exists for moments like this."

The first article charges Trump for pushing Ukraine to announce probes into former Vice President Joe Biden, his son Hunter Biden and Democrats at the same time he was withholding nearly $400 million in military aid and an official White House visit for Ukrainian President Volodymyr Zelenskiy. The second article charges Trump with obstructing the House's investigation into that conduct.

"If the Senate blesses this slapdash impeachment, if we say from now on this is enough, then we invite an endless parade of impeachment trials," he said.

Trump also expressed disdain over the idea that Democrats may not immediately submit the articles, tweeting on Thursday, "Now the Do Nothing Party want to Do Nothing with the Articles & not deliver them to the Senate, but it's Senate’s call!"

"The Senate shall set the time and place of the trial," he said. "If the Do Nothing Democrats decide, in their great wisdom, not to show up, they would lose by Default!"

"Pelosi feels her phony impeachment HOAX is so pathetic she is afraid to present it to the Senate, which can set a date and put this whole SCAM into default if they refuse to show up!" Trump tweeted. "The Do Nothings are so bad for our Country!"

A senior White House official told NBC News that administration officials are "perplexed" by Pelosi's calculation. A second senior White House official said it amounted to an "abuse of power" and "theatrics."

"Pelosi doesn't dictate what happens in the Senate," the official said. "She can’t hold (the articles) hostage to negotiate the terms in the Senate."

The official added that "the House’s job is finished." A third White House official told NBC News the White House sees it as "insane" that Pelosi would hold the articles.

Schumer spoke on the Senate floor moments after McConnell, excoriating the top Republican for "proudly" saying he had "no intention to be impartial" in the trial. He said of his Senate counterpart's earlier evisceration of Democrats' impeachment push: "What hypocrisy."

"Leader McConnell accused the House Democrats of an obsession to get rid of President Trump," Schumer said. "This, from the man who proudly declared his 'number one goal' was to make President Obama a one-term president."