Trump this afternoon kicked off a self-congratulatory vaccine "summit" to tout the speed at which COVID-19 vaccines were produced -- speaking at the same time Biden was introducing his key health appointments and nominees.

The room in the Eisenhower Executive Office Building on the White House complex was packed for the three-hour event, and it appeared almost everyone was wearing a mask, save for Trump.

Asked why no members of the Biden transition were invited to participate, the president falsely claimed he won the election and that he won key swing states where Biden actually was victorious.

“We’re gonna have to see who the next administration is because we won in those swing states -- and there was terrible things that went on. So we’re gonna have to see who the next administration is,” Trump said. “But whichever the next administration is will really benefit by what we’ve been able to do with this incredible science.”

“We were rewarded with a victory,” Trump continued. “Let's see whether or not somebody has the courage -- whether it's legislatures or a justice of the Supreme Court or a number of justice of the Supreme Court. Let's see if they have the courage to do what everybody in this country knows is right.”

To date, Trump, his campaign and its allies have seen at least 38 defeats in court.

-ABC News' Ben Gittleson and Jordyn Phelps

Republicans and Democrats on the congressional committee planning next month's inauguration squabbled Tuesday morning over the election results, with Republicans voting against a measure from House Majority Leader Steny Hoyer acknowledging Biden's victory.

"I made a motion that the committee notify the American people that it is preparing for the inauguration of Joseph Biden and Kamala Harris, and in consultation with them and health experts are doing so to protect the health of our people," Hoyer told reporters after the meeting. "That motion was defeated three to three."

All three Republicans on the panel -- Senate Majority Leader Mitch McConnell, Senate Rules Committee Chairman Roy Blunt and House Minority Leader Kevin McCarthy -- voted against the measure, while Democrats on the panel -- Hoyer, House Speaker Nancy Pelosi and Sen. Amy Klobuchar, D-Minn. -- voted in favor.

Even as they refuse to acknowledge Biden's victory, Republicans called Hoyer's move a stunt that has no bearing on planning the inauguration: They are already working with Biden's inaugural committee, and the measure wasn't relevant to the day's meeting.

“It is not the job of the Joint Congressional Committee on Inaugural Ceremonies to get ahead of the electoral process and decide who we are inaugurating. The JCCIC is facing the challenge of planning safe Inaugural Ceremonies during a global pandemic," Blunt said in a statement. "I would hope that, going forward, the members of the JCCIC would adhere to the committee’s long-standing tradition of bipartisan cooperation and focus on the task at hand.”

-ABC News' Benjamin Siegel

Dr. Rochelle Walensky, chief on infectious diseases as Massachusetts General who was tapped as Biden's pick to lead the Centers for Disease Control and Prevention, said her work on the HIV/AIDS pandemic brought her to this moment and said she is “honored” to serve an administration that will let science lead.

"I've dedicated my career ever since to researching and treating infectious diseases, and to ending the HIV/AIDS crisis for good. Now a new virus is ravaging us. It's striking hardest once again at the most vulnerable: the marginalized, the underserved," she said. "The pain is accelerating. Our defenses have worn down. We are losing life and hope at an alarming rate."

Walensky said she never anticipated taking on the role in government but compared the nation to a dying patient, said it's her calling as a doctor to respond.

"Every doctor knows that when a patient is coding, your plans don't matter. You answer the code. And when the nation is coding, if you are called to serve, serve. You run to take care of people, to stop the bleeding, to stabilize, to give them hope and a fighting chance to come back stronger," she said.

Director of the National Institute of Allergy and Infectious Diseases Dr. Anthony Fauci, who will stay on Biden's COVID-19 equity task force and take on the elevated role of chief medical adviser, appeared virtually at Biden's rollout and expressed support for Biden's initiatives around masks and vaccinations in his first 100 days in office.

"I believe, as you do, that in the fight against this pandemic, we must lead with science and that a key piece of our ongoing work is communicating consistently with the American people," Fauci began.

"Whether it's maintaining social distancing and not congregating indoors, or the 100-day challenge you described on masking or to get as many people vaccinated as possible, these actions are bold, but they are doable and essential to help the public avoid unnecessary risks, to help us save lives, reopen schools and businesses and to eventually beat the pandemic," he continued.

Acknowledging he's dealt with many public health crises in his career, Fauci said the COVID-19 pandemic is "the toughest one we have ever faced as a nation," and repeated Biden's warnings that a dark winter is ahead.

"The road ahead will not be easy. We have got a lot of hard and demanding work to do in the next year, but as we have done during previous crises, I also know we can get through this pandemic together as a nation," Fauci added, thanking Biden for the opportunity to serve in this capacity.

Fauci explained he wasn't able to attend the event in-person because his colleague at the NIAID is receiving the Nobel Prize in medicine Tuesday.

Trump reached out to Pennsylvania State Speaker of the House Brian Cutler last week asking about the legislature possibly overturning the election as part of his ongoing and apparent pressure campaign to have GOP-controlled legislatures flip results in his favor in battleground states he lost.

Mike Straub, a spokesman for Cutler, confirmed to ABC News reporting in The New York Times that Trump asked what options were available to the legislature on the phone call.

“Cutler made it very clear what power the legislature has and does not have," Straub told ABC News, adding he is "not aware of the President explicitly asking to turnover [sic] the election results."

Straub separately told ABC News that he was not present for the conversations between Cutler and the president, but he was briefed.

"The president wanted to know what options were available to the legislature to address those concerns... Speaker Cutler was very clear in explaining what power the legislature has and does not have within our state Constitution," Straub said. "One remedy the Trump campaign is seeking in a court case involves the legislature seating electors -- Speaker Cutler explained the legislature does not have that authority."

Cutler separately signed onto a resolution last week imploring Pennsylvania Republicans in Congress to officially contest the election results in January. While this has happened in the past, including over the election of George W. Bush, it is highly unlikely to overturn the election results.

The Supreme Court may decide Tuesday to take up a challenge by Pennsylvania Republican Rep. Mike Kelly over the constitutionality of mail-in voting, but legal experts have told ABC News that is a long shot. With Tuesday being the constitutionally mandated "safe-harbor" deadline for electors, all legal challenges are meant to be resolved by the end of the day, thus ensuring the correct electors will cast their votes in statehouses on Dec. 14.

-ABC News' Alex Hosenball