With all new senators having been sworn in, Majority Leader Mitch McConnell welcomed the new members on the Senate floor.

"To say the 117th congress convenes at a challenging time would indeed be an understatement. From political divisions to a deadly pandemic to adversaries around the world the hurdles before us are many and they are serious, but there are also plenty of reasons for hope," McConnell said.

The Senate also passed a series of administrative resolutions and standing orders for the new Congress -- including an agreement to Wednesday as a the date to count electoral votes. It's a date already set, but this formalizes it.

In his welcoming remarks, McConnell urged members to remember their oath to the Constitution.

"We gavel in today like 116 prior Senates have gaveled in before us with plenty of disagreements and policy differences among our ranks but all -- all swearing the same oath to support and defend the same Constitution," McConnell said. "All loving the same country and all of us committed to do what we can to leave behind an even stronger nation than the one we've been blessed to inherit."

The Senate stands adjourned until Wednesday.

-ABC News' Allison Pecorin

Wisconsin Democrat Rep. Gwen Moore will participate in Sunday’s opening day events –- including the House speaker’s vote, according to her office, after testing positive for COVID-19 just six days ago.

Republicans complained that her presence “certainly seems to be in violation of the (Office of the Attending Physician) quarantine guidance,” and wonder how it was safe for her to travel to Washington after her diagnosis.

A senior Democratic aide did not immediately respond to an inquiry questioning whether special accommodations were being made for Moore, whose office also has not yet answered inquiries regarding how she traveled to Washington following her infection.

One Democratic member, who said he received his first dose of the COVID-19 vaccine last Tuesday, told ABC News that he is “staying clear of everyone,” pivoting to observe that some Republicans are at the Capitol and not wearing masks.

Speaker Nancy Pelosi, whose path to the speakership is narrow with such a slim majority in the new Congress, will depend on Moore’s support to keep her position.

After opening the 117th Congress with the prayer and pledge, the House has initiated a quorum call to establish sufficient attendance ahead of the vote for speaker later in the afternoon. Lawmakers are appearing in groups of 72, arranged by alphabetical order of their last names.

-ABC News' John Parkinson and Benjamin Siegel

The Senate floor is open and Vice President Mike Pence is presiding over the swearing in of the new Senate.

Senators are presenting themselves in pairs -- in alphabetical order and accompanied by the other senator who represents their state -- where a masked Pence is administering the oath to each pair. The first pair of senators sworn in, Sen. Cory Booker, D-N.J., and Shelly Moore-Capito, R-W.Va., each elbow bumped Pence after taking the oath.

The chamber appears almost entirely full and members are applauding after each administered oath.

The Senate will welcome six new members: Cynthia Lummis, R-Wyo., Ben Ray Lujan, D-N.M., John Hickenlooper, D-Colo,, Roger Marshall, R-Kan., and Bill Hagerty, R-Tenn. Sen. Mark Kelly, D-Ariz., was sworn in late last year.

Two Senate seats remain outstanding pending the Georgia runoff elections on Tuesday. Sen. Kelly Loeffler will maintain her seat because it was an appointment, but Sen. David Perdue's term expires as soon as the new members are sworn in.

-ABC News' Allison Pecorin

The 117th session of Congress will begin with both chambers meeting at noon, as required by the Constitution.

New members of the House and Senate will be sworn in under unusual circumstances given the pandemic, with social distancing and fewer family members and supporters in attendance.

Because control of the Senate hinges on the Georgia Senate runoffs, Republicans will begin the new Congress with control of the chamber and a 51-seat majority. The seat of Sen. David Perdue, R-Ga., will be vacant until a winner is formally certified in Tuesday's runoff election.

Sunday afternoon, the House will elect a speaker.

Nancy Pelosi is expected to win with the narrowest of margins, given Democrats’ historically slim majority, but the vote is expected to take longer than last year because of the coronavirus precautions that require lawmakers to enter the chamber in waves.

-ABC News' Mariam Khan and Benjamin Siegel

Following a briefing with his COVID-19 advisory team on Tuesday, Biden is expected to continue his criticism of the Trump administration in afternoon remarks on the coronavirus pandemic from Wilmington, Delaware, and home in on what his team has characterized as the lagging pace of vaccine distribution.

According to a transition official, Biden will provide an update on the current state of the pandemic and give a dire prediction that, tragically, infection and death rates will rise in the coming weeks. Biden is also expected to address the current administration falling short on its pace for vaccinations, the official said, as well as his plan to get 100 million vaccinations in 100 days.

Biden on Monday slammed the Trump administration for, he said, leaving security agencies "hollowed out" and for creating "roadblocks" for his transition team seeking access to key national security information -- a comment that acting Defense Secretary Christopher Miller has pushed back on, saying the Biden team has already been given more interviews and documents than they initially requested.

Vice President-elect Kamala Harris and her husband, Doug Emhoff, on Tuesday morning are slated to receive their first doses of the COVID-19 vaccine in Washington, D.C., where Harris may also comment on the incoming administration's vaccine distribution plans.

Trump, meanwhile, continued to contest the election on Twitter Tuesday morning -- with three weeks until Biden's inauguration -- criticizing Republican leadership as "pathetic," saying they "only want the path of least resistance" and "only know how to lose." He also attacked Republican lawmakers over their handling of the defensing funding bill as the Senate is expected to override Trump's presidential veto for the first time in his presidency by the end of the week.

After Trump changed course on Sunday and signed the coronavirus relief and government funding bill to avert a shutdown -- though not in time to prevent unemployment benefits to millions of Americans from lapsing -- the House of Representatives on Monday approved Trump's call to increase the coronavirus relief payments from $600 to $2,000.

But its fate in the Senate is uncertain. Senate Majority Leader McConnell has declined to reveal how he will proceed or even whether he’ll bring the proposal up for a vote. Democrats are seizing the opportunity to force Republicans into a difficult position -- either backing or defying Trump.

-ABC News' Molly Nagle and Ben Gittleson