The huge volume of mail ballots - more than 46 million have already been cast - could take days or weeks to tally, experts say, meaning that a winner might not be declared the night of Nov. 3, when polls close.
"It would be very, very proper and very nice if a winner were declared on Nov. 3, instead of counting ballots for two weeks, which is totally inappropriate and I don't believe that that's by our laws," Trump told reporters at the White House before leaving for campaign rallies in three states. "We'll see what happens."
Trump has repeatedly and without evidence suggested that an increase in mail voting will lead to an increase in fraud, although election experts say that is rare in U.S. elections. Mail voting is a long-standing feature of American elections, and about one in four ballots was cast that way in 2016.
Democratic officials, activists and voters have voiced deep anxieties that Trump will not accept the outcome if he loses. Biden has called it his biggest fear.
Democrats are voting early in greater numbers than Republicans this year, according to data from the Elections Project, but some states do not allow officials to begin counting those ballots until the polls close.
Republicans in a series of court battles across the United State are trying to limit the time and opportunities voters have to send in ballots.
In a court victory for Trump, the Texas Supreme Court ruled on Tuesday that the state's Republican governor may limit drop-off sites for election ballots to one per county. The ruling reversed an appeals court decision from last week.
Nearly 8 million Texans had cast ballots as of Tuesday, approaching 90% of the state's entire 2016 vote - a higher percentage than any other state in the country, according to the Elections Project.
With a week to go, Biden leads Trump nationally by 10 percentage points, according to a Reuters/Ipsos poll conducted from Friday to Tuesday. The national online survey found that 52% of likely voters said they were backing Biden, while 42% were voting for Trump.
The race is tighter in battleground states including North Carolina, Florida and Arizona where the election might be decided. A Reuters/Ipsos poll on Tuesday showed Biden with a 52%-43% lead over Trump in Michigan, with the two statistically tied in North Carolina.
Biden's visit to Georgia was a show of optimism that his campaign can end the presidency of Trump, who has overseen the battering of the country by the coronavirus, an increase in racial tensions and the fraying of ties with European allies.
Georgia has not supported a Democrat in a U.S. presidential election since 1992.
"I'm running as a proud Democrat, but I will govern as an American president. I'll work with Democrats and Republicans. I'll work as hard for those who don't support me as for those who do," Biden said in Warm Springs, the vacation home of former President Franklin D. Roosevelt, the Democrat who led the nation during the Great Depression and World War Two.
"Something’s happening here in Georgia and across the country," Biden said later in Atlanta. "We win Georgia, we win everything."
Trump visited Michigan, Wisconsin and Nebraska on Tuesday before stopping overnight in Nevada.
"I will deliver record prosperity, epic job growth and a safe vaccine that eradicates the virus and quickly ends the pandemic," Trump said at his rally in Omaha, Nebraska
The Trump campaign said its official website was defaced on Tuesday and that it was working with law enforcement to investigate the source of the attack. In a statement, the campaign said the site had been restored and there was "no exposure to sensitive data because none of it is actually stored on the site."
The 2020 presidential campaign has been unlike any other, conducted amid a raging coronavirus pandemic that has so far caused more than 225,000 U.S. deaths and become the top issue in the election.
Nearly half a million people in the United States have contracted the novel coronavirus in the past seven days, according to a Reuters tally, as cases and hospitalizations set records in hot spots in the Midwest. More than 5,600 people died from the virus nationwide in the past week.
In another show of confidence for Biden, former New York Mayor Michael Bloomberg said on Tuesday he would spend around $15 million on television advertising in Texas and Ohio in the coming days.
Former President Barack Obama was also back on the trail in Florida on Tuesday to boost Biden, who was his vice president.
At a drive-in rally in Orlando, Obama urged Democrats to vote in large numbers to avoid a repeat of the 2016 election when Trump won the battleground state and defeated Hillary Clinton.
"We have to leave no doubt. We can't be complacent," he said. "We were complacent last time. Folks got a little lazy, folks took things for granted, and look what happened. Not this time, not in this election."
(Reporting by Jeff Mason and Ernest Scheyder; Additional reporting by James Oliphant, Costas Pitas, Daphne Psaledakis and Susan Heavey; Writing by Alistair Bell and John Whitesides; Editing by Scott Malone, Howard Goller and Peter Cooney)