Speaker Nancy Pelosi said on Friday that the House managers she appointed to prosecute President Trump’s impeachment case were preparing to take their charge to trial in the Senate, but she refused to offer a timeline for when they would proceed.

At a news conference inside the Capitol, the speaker made clear that her first priority was ensuring the security of the building and lawmakers ahead of President-elect Joseph R. Biden Jr.’s inauguration next week.

Growing emotional at points as she recounted seeing the image of an insurrectionist in a “Camp Auschwitz” sweatshirt, the speaker said accountability would soon follow for Mr. Trump, members of the violent mob he incited who stormed the building last week and far-right members of Congress if they were found to have aided the insurrection.

“One week ago, on Jan. 6, there was an act of insurrection perpetrated on the Capitol of the United States, incentivized by the president of the United States,” Ms. Pelosi said. “One week later, Wednesday to Wednesday, that president was impeached in a bipartisan way by the House of Representatives. So urgent was the matter. They are now working on taking this to trial and you will be the first to know when we are going over there.”

The comments came as Ms. Pelosi fielded questions for the first time since the House impeached Mr. Trump on Wednesday for inciting the violent insurrection at the Capitol as he sought to overturn Mr. Biden’s election victory. The attack came as members of Congress and the vice president met to formalize the result.

Behind the scenes, Democrats, poised to take unified power in Washington next week for the first time in a decade, were working with Republican leaders to try to find a proposal to allow the Senate to split time between the impeachment trial of Mr. Trump and consideration of Mr. Biden’s agenda, including his cabinet nominees and a $1.9 trillion economic recovery plan he proposed on Thursday to address the coronavirus. But they were virtually silent in public about their plans.

Although Senator Mitch McConnell, Republican of Kentucky and the majority leader, has privately told advisers that he approves of the impeachment drive and believes it could help his party purge itself of Mr. Trump, he refused to begin the proceedings this week while he is still in charge. That means the trial will not effectively start until after Mr. Biden is sworn in on Wednesday, officials involved in the planning said.

It has also left Democrats weighing whether to bring their case to the Senate immediately, potentially handicapping Mr. Biden’s first few days in office and distracting from his inauguration, or waiting until a few days after he is sworn in. The latter option may be more appealing to Mr. Biden, but it could undercut Democrats’ argument that Congress must move urgently to impeach and try Mr. Trump.

With Republicans fractured after the president’s exhortations to supporters to reject his defeat inspired a rampage, many of them were trying to gauge the dynamics of a vote to convict Mr. Trump. Doing so would open the door to disqualifying him from holding office in the future.

A cautionary tale was playing out in the House, where a faction of Mr. Trump’s most ardent allies was working to topple Representative Liz Cheney of Wyoming, the No. 3 Republican, from her leadership post. Ms. Cheney had joined nine other members of the party who voted with Democrats to charge the president with “incitement of insurrection.”

Emily Cochrane contributed reporting.

— Nicholas Fandos and Catie Edmondson The New York Times