WASHINGTON - President Donald Trump signaled 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 votes solidifying Joe Biden's victory. 

In a Fox News interview that aired Sunday morning, Trump repeated his false claims of election fraud and said his legal team will continue to pursue challenges, despite the Supreme Court's recent dismissal of a long-shot bid to overturn the results in four states 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. "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; Trump won 232.

Trump's comments came a day before electors meet in each of the 50 states and the District of Columbia to cast their ballots for president and vice president.

The electors are expected to follow the vote of their state. After voting, they must sign six certificates, one of which is submitted to the president of the Senate, currently Vice President Mike Pence. Both chambers of Congress - the House and the Senate - will meet in joint session on Jan. 6 to officially count the votes.

In the Fox News interview, Kilmeade outlined the process and asked Trump how it 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."

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

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

Once the voting is complete, Biden is expected to deliver remarks Monday night in Wilmington, Del., on "the electoral college vote certification and the strength and resilience of our democracy," according to his transition team.

Even if Trump's efforts to overturn Biden's victory come up short, some of the president's allies have suggested in recent days that they will try to change how states conduct future elections.

"I think the campaign is taking our arguments that we tried to get in front of the U.S. Supreme Court - they are now going to take those, I think, state by state," Texas Attorney General Ken Paxton, a Republican who spearheaded the lawsuit that was dismissed by the Supreme Court, said in an interview on "Sunday Morning Futures" on Fox.

Paxton added that "they are legitimately good constitutional arguments that don't depend on actually proving every little instance of fraud."

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% of registered voters believe that the election is over and that it is time to move on. But 75% of Republicans said that the election is not over and that it should still be contested. About 18% 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 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 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."

Some Republicans have worried that Trump's efforts to undermine the legitimacy of the presidential election could deter some GOP voters from going to the polls Jan. 5 in Georgia, which is holding two Senate runoffs that could determine which party controls the upper chamber.

Sen. David Perdue, R-Ga., who along with Sen. Kelly Loeffler, R-Ga., is running for reelection, urged Republicans to cast their ballot, even if they do not trust the system.

"We're doing everything we can with the secretary of state's office, the attorney general's office and in the courts to make sure that what we now know happened potentially in November won't happen in January," Perdue said on "Sunday Morning Futures." "So, we want people to have the confidence to get out and vote. But whether they do or not, they still have to vote."

Perdue is facing Democrat Jon Ossoff, while Loeffler is running against the Rev. Raphael Warnock, a Democrat.

More than half of the House Republican conference signed the Texas lawsuit that sought to overturn the results of the election in Georgia, Michigan, Pennsylvania 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." "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."

Rep. Cedric 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 CBS's "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 he lost this election."

Among the Republicans who have urged Trump to concede is former New Jersey Gov. Chris Christie, who on Sunday 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 term, 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."

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