Mr Trump began his Sunday in Nevada, making a rare visit to church before a fundraiser and an evening rally in Carson City.
Once considered a battleground state, Nevada has not swung for a Republican presidential contender since 2004.
The rally drew thousands of supporters who sat elbow to elbow, cheering Mr Trump and booing Mr Biden and the press.
The vast majority wore no masks to guard against the coronavirus, though cases in the state are on the rise with more than 1,000 new infections reported on Saturday.
The president, as he often does, warned that a Biden election win would lead to further lockdowns, and at one point appeared to mock the former US vice president for saying he would listen to scientists.
“He’ll listen to the scientists,” Mr Trump said. “If I listened totally to the scientists, we would right now have a country that would be in a massive depression.”
Mr Biden, a practicing Catholic, attended Mass in Delaware before campaigning in North Carolina, where a Democrat has not won in a presidential race since Barack Obama in 2008.
Both candidates are trying to make inroads in states that could help secure a path to victory, but the dynamics of the race are remarkably stable.
Mr Biden enjoys a significant advantage in national polls, while carrying a smaller edge in battleground surveys.
Wear a mask. Wash your hands. Vote out Donald Trump.
Advertisement— Joe Biden (@JoeBiden) October 19, 2020
Earlier in the day, Mr Trump sat in the front row at the non-denominational International Church of Las Vegas as the senior associate pastor, Denise Goulet, said God told her early that morning that the president would secure a second term.
She said: “At 4.30, the Lord said to me: ‘I am going to give your president a second win,'” she said, telling Mr Trump: “You will be the president again.”
Mr Trump spoke briefly, saying “I love going to churches” and that it was “a great honour” to attend the service. He dropped a wad of 20 dollar bills in the collection plate before leaving.
The message was far different in both style and substance later in the day, when Mr Biden attended a virtual discussion with African American faith leaders from around the country.
Mr Biden held up a rosary, which he said he carries in his pocket every day, and described it as “what the Irish call a prisoner’s rosary”, since it was small enough to be smuggled into prisons.
“I happen to be a Roman Catholic,” Mr Biden said. “I don’t pray for God to protect me. I pray to God to give me strength to see what other people are dealing with.”
Earlier, at a drive-in rally in Durham, North Carolina, Mr Biden focused heavily on promoting criminal justice changes to combat institutional racism and promised to help build wealth in the black community.
He noted that Mr Trump had said at one of his rallies that the country had turned the corner on the pandemic.
Mr Biden said of the president: “As my grandfather would say, this guy’s gone around the bend if he thinks we’ve turned the corner. Turning the corner? Things are getting worse.”
In addition to public polling that indicates Mr Biden has an edge, the former vice president enjoys another considerable advantage over Mr Trump: money.
The president raked in $12 million (€10.2 million) during a fundraiser on Sunday afternoon at the Newport Beach home of top Republican donor and tech mogul Palmer Luckey, which also featured a performance by the Beach Boys.
But over the past four months, Mr Biden has raised over $1 billion (€850 million), a massive amount of money that has eclipsed Mr Trump’s once-overwhelming cash advantage.
That has become apparent in advertising, where Mr Biden and his Democratic allies are on pace to spend twice as much as Mr Trump and the Republicans in the closing days of the race, according to data from the ad tracking firm Kantar/CMAG.
Though Mr Trump has pulled back from advertising in Midwestern states that secured his 2016 win, he has invested heavily elsewhere, including North Carolina, where he is on pace to slightly outspend Mr Biden in the days ahead.
In Nevada, which Mr Trump came close to winning in 2016, Democrats are set to outspend him in the closing days by more than three-to-one.
How the hell can we be tied? What’s going on? We get these massive crowds. He gets nobody. It doesn’t make sense!
Mr Trump’s visit to the state is part of an aggressive schedule of campaign events, where he has leaned heavily into fear tactics.
At the Carson City rally, he relived fond moments from his 2016 campaign against Hillary Clinton, revisited his long-running feud with NFL players and went on an extended rant about water management policy, which he blamed for people having to “flush their toilet 15 times”.
He also claimed that, if Mr Biden was elected, he would mandate new lockdown measures that would make Carson City “a ghost town” and “the Christmas season will be cancelled”.
As he surveyed his crowd, Mr Trump expressed disbelief that he could possibly be tied (in fact he is losing, according to public polls) to Mr Biden in the state.
“How the hell can we be tied?” he asked. “What’s going on? We get these massive crowds. He gets nobody. It doesn’t make sense!”
Mr Biden started his day with Mass in Delaware at St Joseph’s on the Brandywine, as he does nearly every week. He and his wife, Jill, entered wearing dark-coloured face masks.
The church is a few minutes’ drive from Mr Biden’s home. His son Beau, who died of brain cancer in 2015, is buried in the cemetery on its grounds. Joe and Jill Biden visited the grave after the service.
If elected, Mr Biden would be only the second Roman Catholic president in US history and first since John F Kennedy.
The former vice president speaks frequently about his faith and its importance in his life.
