WASHINGTON — President Donald Trump’s impeachment trial is likely to start after Joe Biden’s inauguration, and the Republican leader, Mitch McConnell, is telling senators their decision on whether to convict the outgoing president over the U.S. Capitol riot will be a “vote of conscience.”

The timing for the trial, the first of a president no longer in office, has not been set. But House Speaker Nancy Pelosi made it clear Friday that Democrats intend to move swiftly on President-elect Joe Biden’s $1.9 trillion COVID aid and economic recovery package to speed up vaccinations and send Americans relief. Biden is set to take the oath of office Wednesday.

Pelosi called the recovery package a “matter of complete urgency.”

Meanwhile, Vice President Mike Pence has called his soon-to-be successor Kamala Harris to offer his congratulations, according to two people familiar with the conversation.

It’s the first known contact between the elected members of the outgoing and incoming administrations. Trump has not reached out to Biden and has repeatedly questioned the legitimacy of Biden’s win.

One of the people familiar with the Thursday afternoon conversation described it as a “good call,” with Pence congratulating his successor and offering assistance. They spoke on condition of anonymity to describe the private conversation.

Pence will also attend Biden’s inauguration, which Trump is refusing to attend.

The uncertainty of the scheduling of Trump’s Senate trial, despite the House’s swift impeachment of the president just a week after the deadly Jan. 6 siege, reflects the fact that Democrats do not want the Senate trial proceedings to dominate the opening days of the Biden administration.

With security on alert over the threat of more potential violence heading into the inauguration, the Senate is also moving quickly to prepare for confirming Biden’s nominee for national intelligence director, Avril Haines. A committee hearing is set for Tuesday, signaling a confirmation vote to install her in the position could come swiftly once the new president is in office.

Many Democrats have pushed for an immediate impeachment trial to hold Trump accountable and prevent him from holding future office, and the proceedings could still begin by Inauguration Day. But others have urged a slower pace as the Senate considers Biden’s Cabinet nominees and the newly Democratic-led Congress considers priorities like the coronavirus plan.

Biden has said the Senate should be able this time to split its work, starting the trial and working on legislation and confirmations.

Trump is the only president to be twice impeached, and the first to be prosecuted as he leaves the White House. He was impeached by the House in 2019 over dealings with Ukraine, but the Senate voted in 2020 to acquit.

When his second trial does begin, House impeachment managers say they will be making the case that Trump’s incendiary rhetoric hours before the bloody attack on the Capitol was not isolated, but rather part of an escalating campaign to overturn the November election. It culminated, they will argue, in the Republican president’s rally cry to “fight like hell” as Congress was tallying the Electoral College votes to confirm he’d lost to Biden.

For Republican senators, the trial will be a perhaps final test of their loyalty to the defeated president, and his legions of supporters in their states back home, and their own experiences sheltering at the Capitol as a pro-Trump mob ransacked the building

“These men weren’t drunks who got rowdy — they were terrorists attacking this country’s constitutionally-mandated transfer of power,” said Sen. Ben Sasse, R-Neb., in a statement Friday.

McConnell, who has spent the past days talking to senators and donors, is telling them the decision on whether or not to convict Trump is theirs alone — meaning the leadership team will not work to hold senators in line one way or the other.

Pelosi told reporters Friday that the nine House impeachment managers, who act as the prosecutors for the House, are working on taking the case to trial.

All lawyers and some of Pelosi’s closest allies, the managers have argued that while it is important to turn a new page with the Biden presidency, it is also crucial to reckon with the Capitol violence.

Trump was impeached Wednesday by the House on the single charge, incitement of insurrection, just a week after after the siege. Ten Republicans joined all Democrats in the 232-197 vote to impeach, the most bipartisan modern presidential impeachment.

McConnell is open to considering impeachment, having told associates he is done with Trump, but he has not signaled how he would vote. McConnell continues to hold great sway in his party, even though convening the trial next week could be among his last acts as majority leader as Democrats prepare to take control of the Senate with the seating of two new Democratic senators from Georgia.

No president has ever been convicted in the Senate, and it would take a two-thirds vote against Trump. But a conviction is not out of the realm of possibility, especially as corporations and wealthy donors distance themselves from Trump’s brand of politics and Republicans who stood by his attempt to overturn the election.