Washington (CNN) Senate Majority Leader Mitch McConnell on Friday firmly rejected any idea that House Democrats will be able to dictate the way an impeachment trial of President Donald Trump unfolds.

"Let me clarify Senate rules and Senate history for those who may be confused. First, about this fantasy that the speaker of the House will get to hand design the trial proceedings in the Senate, that's obviously a non-starter," McConnell said in a Senate floor speech.

McConnell also defended his coordination with the White House over the trial.

"We've heard claims that it's a problem that I've discussed trial mechanics with the White House even as my counterpart the Democratic Leader is openly coordinating political strategy with the Speaker, who some might call the prosecution. So it's okay to have consultation with the prosecution, but not apparently with the defendant?"

McConnell made clear that he does not plan to move forward with a trial until the House transmits the articles.

"We can't hold a trial without the articles," he said, adding, "so for now we're content to continue the ordinary business of the Senate" until the articles are sent.

McConnell's remarks kick off the second session of the 116th Congress and mark a return to the impeachment fight after a brief period of relative quiet over the holiday season.

Speaking after McConnell, Senate Minority Leader Chuck Schumer reiterated his call for witnesses at a trial and said that McConnell "intends to act as an executioner of a fair trial."

"Leader McConnell has been clear and vocal that he has no intention to be impartial in this process. Leader McConnell reminds us today and in previous days that rather than acting like a judge and a juror, he intends to act as an executioner of a fair trial. Thankfully the rules of an impeachment trial will be determined by a majority of the senators in this chamber, not by the Republican leader alone," Schumer, a New York Democrat, said.

He went on to say, "the Republican leader hasn't given one good reason why there shouldn't be relevant witnesses or relevant documents. We did not hear one from leader McConnell today or any day," Schumer said.

Schumer argued that the Senate should not wait until the trial is already underway to make a decision on whether to call witnesses.

"When Leader McConnell suggests we have both sides present their arguments and then deal with witnesses, he is essentially proposing to conduct a whole trial and then once the trial is basically over, consider the question of evidence. That makes no sense. That's Alice in Wonderland logic," he said.

Signaling that the Senate trial stalemate has not yet been broken, Schumer said, "It may feel like we are no closer to establishing the rules for a Senate trial then when we last met, but the question, the vital question of whether or not we have a fair trial ultimately rests with a a majority of the senators in this chamber."

The House of Representatives still has not moved to send over the articles of impeachment to the Senate and McConnell said ahead of the holiday recess that the Senate was at an "impasse" about setting the rules of a trial, leaving the status of the trial in limbo as lawmakers left Washington until the new year.

As attention on Capitol Hill turns back to the question of what will happen next in the impeachment saga, lawmakers are also reacting to and are deeply divided over the US airstrike that killed Iran Quds Force commander Qasem Soleimani, paving the way for the possibility that Capitol Hill will be consumed with both a debate over foreign policy and impeachment.

House Speaker Nancy Pelosi, who has declined to send the two articles of impeachment to the Senate until Democrats receive assurances about the structure of the looming trial, hasn't made any recent public remarks about her plans.

On Thursday, she asked on Twitter: "Why won't Trump & McConnell allow a fair trial?," but did not not clarify her intentions moving forward.

McConnell on Friday criticized House Democrats for not having sent the impeachment articles to the Senate, accusing them of delaying for partisan reasons.

"As soon as the partisan impeachment votes had finished, the prosecutors began to develop cold feet. Instead of sending the articles to the Senate, they flinched," McConnell said.

"The same people who just spent weeks screaming that impeachment was so serious and so urgent that it couldn't wait for due process now decided it could wait indefinitely while they checked the political winds and looked for some new talking points," the Majority leader said, adding, "as House Democrats continue their political delay, they're searching desperately for some new talking points to help them deflect blame for what they've done."

This story has been updated with additional developments.