WASHINGTON -- US President Donald Trump was leading in five of six key battleground states, including Florida, while his Democratic rival Joe Biden was projected to win the previously Republican state of Arizona in Tuesday's tight presidential election.

Vote counting was still under way in most states, including the battleground states, but Trump was ready to claim victory in a late night press conference.

"We were ready to win. Frankly, we did win this election," he said in a White House press conference.

As of 2:30 a.m., Trump was projected to have secured 213 electoral votes out of the total 538 against Biden's 220, according to CNN.

Whoever wins a majority of 270 Electoral College votes or more will become the next US president.

Voting began early Tuesday in the small town of Dixville Notch, New Hampshire, where its small population traditionally gathers at the turn of midnight to cast ballots, with the results often declared minutes afterward.

About 150 million, or 62 percent, of the roughly 240 million eligible American voters were expected to cast their ballots in the election, marking the highest voter turnout since 1908, when the turnout rate stood at 65.7 percent.

A record number of more than 101 million Americans voted early -- over 65 million by mail and more than 35 million in early, in-person voting.

With about 75 percent of votes counted in Arizona, Biden had 53.5 percent of the eligible votes, while Trump had 45.1 percent, according to US cable news network CNN.

Arizona is one of the six battleground states, all of which were won by Trump in 2016.

They include Michigan, North Carolina, Pennsylvania and Wisconsin, as well as Florida, that together with Arizona hold 101 electoral votes.

Trump was projected to win Florida with over 51 percent of all votes cast in the state, compared with Biden's 47.7 percent, with about 94 percent of votes counted as of 11:30 p.m.

Biden said he felt good about "where we are" but insisted it was not his place nor that of Trump to declare who won the election, noting the results may take days to come out.

"It ain't over 'till it is over," said Biden, speaking to a group of supporters in Delaware. "We just have to be patient."

Trump had no immediate plans to address the nation about the outcome of the election, the White House said earlier.

In a final pitch, Biden earlier visited Pennsylvania, canvassing from his hometown of Scranton to Philadelphia.

"I promise you this. Although I am running as a proud Democrat, if you elect me, I am going to be an American president," Biden told a group of supporters gathered on a street of Philadelphia, adding that he will not treat Republican states any different from Democrat states.

Trump said he expected to do better this year than four years ago.

"I think we will top it," Trump said in a telephone interview with US cable network Fox News, referring to the 306 electoral votes he won in 2016.

"I think we have a very solid chance of winning," he added.

Later visiting a Republican election campaign headquarters in Arlington, Virginia, Trump said he expected to see the outcome of Tuesday's election later in the day, insisting the voters have the right to know the result on the day of election.

"We have a big night planned. We're going to have a very big night," Trump said.

Unlike in past elections, however, the winner of Tuesday's presidential election may not be declared for days, if not weeks, partly because of the record number of mail-in votes.

Many states do not allow the counting of mail-in ballots until after the end of the election, while some accept late-arriving mail-in votes that are postmarked by the day of the election.

Some also believe Trump may dispute the results should he find himself losing.

He has repeatedly claimed the only way he is going to "lose this election is if this election is rigged," leaving many suspecting that he may challenge the outcome regardless of the vote tally if he does not win.

The race between Trump and Biden is also being closely watched by many countries, including South Korea, as the stark difference between their views on nearly every issue points to drastic changes in how the US will interact with the rest of the world over the next four years.

Trump has vowed to continue putting "America first" as the world's most powerful nation continues to struggle with the COVID-19 pandemic and its economic fallout.

The worst pandemic in decades, and possibly in US history, has consumed nearly all campaign efforts, and whoever wins the election will face a daunting task of keeping Americans safe from the novel virus and preventing the economy from falling into a deep recession.

As of Sunday, more than 9.1 million Americans have been infected by the new coronavirus, while more than 234,000 have died from the infectious disease, according to the US Centers for Disease Control and Prevention.

Both numbers account for around 20 percent of global tallies, while Americans account for only about 3 percent of the world population.

Biden says he will begin to tackle the pandemic from the very first day of his presidency, if elected, but also notes one of the first things he will do as president is to restore his country's leadership in the international community.

The former vice president accuses Trump of undermining the country's relationship with other countries, especially its traditional allies, with his America First policy.

Also at stake in Tuesday's election are 35 Senate seats, as well as all 435 seats in the House of Representatives.

Trump's Republican Party currently has a majority of Senate seats but is defending 23 of the 35 seats up for grabs.

The Democratic Party needs to take four or more seats, in addition to the 12 seats it is defending, for a Senate majority.

The liberal party currently holds a House majority of 232 seats over 197 held by the conservative party.

The winner of the presidential election will be sworn in on Jan. 20 but may face difficulties for years to come without a majority in either house of Congress. (Yonhap)