President Donald Trump signaled over the weekend that he will continue to challenge the results of the 2020 election, even after the electoral college meets Monday in most state capitols to cast its votes.

In a Fox News Channel interview that aired Sunday morning, Trump repeated his false claims of election fraud and said his legal team will keep pursuing challenges despite the Supreme Court's dismissal of a long-shot bid led by the Texas attorney general to overturn the results in four states that President-elect Joe Biden won.

"No, it's not over," Trump told host Brian Kilmeade in the interview, which was taped Saturday at the Army-Navy game at the U.S. Military Academy at West Point. "We keep going, and we're going to continue to go forward. We have numerous local cases. We're, you know, in some of the states that got rigged and robbed from us. We won every one of them. We won Pennsylvania. We won Michigan. We won Georgia by a lot."

Trump lost those swing states and others to Biden, who won 306 electoral votes to Trump's 232.

Kilmeade noted that the electoral college will meet Monday and the ballots will then be transmitted to Congress, which will officially count the votes on Jan. 6. Asked how that process affects his chances for successfully challenging the results, Trump demurred.

"I don't know," he said. "We're going to speed it up as much as we can, but you can only go so fast. They give us very little time."

Asked whether he plans to attend Biden's inauguration next month, Trump declined to say.

"I don't want to talk about that," he said.

Public polling shows that many Republican voters doubt the legitimacy of the 2020 election, prompting some observers to worry that Trump's refusal to concede will further divide the country.

A CBS News poll released Sunday shows that 62 percent of registered voters believe that the election is over and that it is time to move on.

But, notably, 75 percent of Republicans said that they believe the election is not over and that it should still be contested. Just 18 percent of those who voted for Trump in 2020 said they consider Biden the legitimate winner.

Attorney General William Barr, who was appointed by Trump, said earlier this month that he has "not seen fraud on a scale that could have effected a different outcome in the election," undercutting Trump's claims of widespread and significant voting irregularities.

Nonetheless, the president has continued to make unfounded accusations of fraud, calling the election "a sham and a shame" and dismissing concerns that his actions are driving Americans further apart.

"No," Trump told Kilmeade when asked whether he shares those concerns. "I worry about the country having an illegitimate president. That's what I worry about. A president that lost and lost badly. This wasn't, like, a close election. ... I didn't lose. The election was rigged."

By contrast, the CBS News poll showed that Democratic voters do not view Republicans' victories in House and Senate races as fraudulent.

Seventy-eight percent of Democrats, and 87 percent of registered voters overall, believe Republicans legitimately won those races.

More than half of the House Republican conference signed on to the Texas lawsuit that sought to overturn the results of the election in Georgia, Pennsylvania, Michigan and Wisconsin. One of those House Republicans, Minority Whip Steve Scalise of Louisiana, suggested Sunday morning that it will still be too early to call Biden president-elect even after the electoral college meets Monday.

"Let the legal process play out," Scalise, the No. 2 Republican in the chamber, said in an interview on "Fox News Sunday." "But if you want to restore trust by millions of people who are still very frustrated and angry about what happened, that's why you've got to have the whole system play out."

Few members of the Trump administration have acknowledged Biden's win, as well. Health and Human Services Secretary Alex Azar, like others, has repeatedly declined to call Biden president-elect. But during an interview Sunday, he appeared to affirm that a new administration will take office next month.

On CBS News's "Face the Nation," host Margaret Brennan asked Azar whether he believes a Biden administration will be able to meet the goal of 100 million coronavirus vaccinations in the United States by the end of February.

"If they carry forward with the plans that we've put in place, 100 million shots in arms by the end of February is very much in scope," Azar said.

Rep. Cedric L. Richmond, D-La., who will soon be joining the Biden administration as a senior adviser, on Sunday played down the significance of Republicans' refusal to acknowledge Biden's win. In an interview on "Face the Nation," Richmond argued that "this is just a small portion of the Republican conference" that is hesitant to publicly recognize Biden's victory "because they are scared of (Trump's) Twitter power and other things."

"They recognize Joe Biden's victory," Richmond said. "All of America recognizes Joe Biden's victory. ... I talk to Republican members of Congress all the time, and they say one thing privately; they say another thing publicly. But the one thing I will tell you is they realize (Trump) lost this election."

Among the Republicans who have urged Trump to concede is former New Jersey governor Chris Christie, who on Sunday sharply criticized the president's continuing efforts to overturn the election results.

"The reason the Supreme Court is not taking this is not because of a lack of courage," Christie said on ABC News's "This Week." "It's for the same reason that every court has thrown this out: It's a lack of evidence and a lack of any type of legal theory that makes any sense."

Sen. Lamar Alexander, R-Tenn., who is retiring at the end of the year, said there should not be any doubt after Monday about who won the presidential election.

"I mean, the states have counted, certified their votes," Alexander said on NBC News's "Meet the Press." "The courts have resolved the disputes. It looks very much like the electors will vote for Joe Biden. And when they do, I hope that he puts the country first - I mean, the president - that he takes pride in his considerable accomplishments, that he congratulates the president-elect and he helps him get off to a good start, especially in the middle of this pandemic."

The senator added: "We need to not lose one day in the transition in getting the vaccine out to everybody who needs it."

The Washington Post’s Craig Timberg, Tory Newmyer and Paulina Firozi contributed to this report.