Earlier Hillary Clinton's campaign manager spoke at a planned rally also in New York and said the election is too close to call.
John Podesta urged supporters of the Democratic presidential hopeful to go home as counting in the election was still going on.
So no concession speech will be made by Mrs Clinton despite Donald Trump projected to be just 26 Electoral College votes away from victory.
Enthusiasm grew among supporters of the Republican presidential nominee at his election night headquarters as he led in the race for the White House.
Supporters wearing red caps emblazoned with Trump's slogan "Make America Great Again" clapped and cheered as network announcers read results.
Polls released earlier in the day showed Mrs Clinton with a slight lead over Mr Trump but Mr Trump has taken the key swing states of Ohio and North Carolina with several key states still undeclared in the presidential election.
Both Mr Trump and his Democratic rival Hillary Clinton scored victories in states where they were expected to win. Mr Trump captured conservative states in the south and midwest, while Mrs Clinton swept several states on the east coast and Illinois in the midwest.
Mrs Clinton is projected to win in Illinois, New York, New Jersey, New Mexico, Massachusetts, Maryland, Rhode Island, Delaware, Colorado, California, Nevada, Hawaii, Vermont, Maine and Washington DC with Mr Trump projected to take Indiana, West Virginia, Kentucky, Arkansas, Texas, Oklahoma, Tennessee, Mississippi, Missouri, South Carolina, Alabama, South Dakota, North Dakota, Wyoming, Nebraska, Montana, Idaho, North Carolina, Utah, Ohio, Florida.
CBS News has projected 218 Electoral College votes for Mrs Clinton so far with Mr Trump winning 245.
Full RTÉ coverage of US Election results
Wall Street Journal Columnist Peggy Noonan described the unfolding results as "a kind of uprising, a kind of revolt, a kind of pushback against the elites, the establishment of both parties".
She said there is a sense of "protected people in America and unprotected people" and the "unprotected just pushed back in a way that strikes me as deeply historic".
After a long and exceptionally negative campaign, the battle focused on the character of the candidates.
Mrs Clinton, 69, a former US secretary of state, and Mr Trump, 70, New York businessman, accused each other of being unfit to lead the United States against challenges like an arduous economic recovery, Islamist militants and the rise of China.
The campaign ended in the same angry tone it began, with Mr Trump calling his rival a "phoney" and Mrs Clinton accusing him of splitting the country.
Both candidates raced through several battleground states yesterday in a last-ditch attempt to encourage their supporters to show up and vote.
Mrs Clinton sought to capture more support from Latinos, African-Americans and young people, while Mr Trump looked to win over disaffected Democrats and rev up a middle class that he said has been sidelined by the political establishment.
An early exit poll showed some 62% of voters decided before September which candidate they would back, according to CNN.
Only 12% decided over the past week - suggesting that recent revelations about the FBI's investigation into Mrs Clinton's emails and Mr Trump's lewd comments about women and accusations of inappropriate sexual behaviour did not have much impact on Americans as they went to the polls, the broadcaster said.
The CNN exit poll results suggested neither candidate was particularly popular. Only 42% said they "strongly favoured" the candidate they voted for.
The two presidential hopefuls are spending election night in New York, staging events barely more than two kilometres apart from each other.
Mrs Clinton will address supporters at the Javits Centre in Manhattan, while Mr Trump has billed his speech at the Hilton Midtown hotel as a "victory party".
There was a heavy police presence in New York after US authorities received intelligence of a possible pre-election al Qaeda attack.
Security was heightened at Trump Tower on Fifth Avenue by parking trucks filled with sand outside the building.
More than 5,000 police officers were deployed across New York City to keep order on election night.
Mrs Clinton is aiming to become the first female president in US history, while Mr Trump hoped his pledge to Make America Great Again would win over voters in key swing states.
Mr Trump, who has been dogged by allegations of misogyny and sexual misconduct, has targeted battleground states in an effort to get the 270 Electoral College votes he needs to become one of the most unlikely victors of a presidential race.
Economy tops list of worries facing American voters - Reuters/Ipsos
The economy, terrorism and healthcare ranked as the top three concerns facing Americans casting ballots in the presidential election, according to an early reading from a Reuters/Ipsos States of the Nation poll.
The poll of about 35,000 people found that 25% of voters picked the economy as the "most important problem."
Another 14% named "terrorism/terrorist attacks" and 13% picked healthcare.
By contrast, the economy was the number one concern for 46% of American voters in 2012, according to the Reuters/Ipsos national tracking poll four years ago.
Almost nobody listed terrorism as a top concern in 2012, and 8% listed healthcare as the top worry.
A signature Trump issue, immigration, was chosen by 7% of voters as the most important issue in the poll.
Two-thirds of US voters say they back some gun control - Reuters/Ipsos
Two-thirds of Americans voting in the election favour moderate or strong gun control measures, according to the Reuters/Ipsos poll, up from 59% who said so in 2012.
Mr Trump has been a vocal opponent of increased limits on American gun ownership, while Mrs Clinton has advocated for an assault weapons ban and comprehensive background checks on would-be gun owners, following a slew of deadly mass shootings in the United States.
The survey found that Americans' views on abortion - another divisive issue in American politics - has not changed significantly since 2012, with 39% of voters saying it should be illegal.
Mr Trump opposes abortion and has said it should be punished while Mrs Clinton believes it should remain legal.
Republicans defend US House majority, Senate on razor's edge
Republicans will maintain their six-year control over the US House of Representatives, according to early network projections, as the party also put up an unexpectedly tough fight to protect its majority in the US Senate.
The ABC and NBC television networks said Republicans, as widely projected in opinion polls, would keep control of the House, which has been in their hands since 2011.
Winners had been declared so far in 16 Senate races, with Democrats making a net gain of only a single seat so far, but some other opportunities for them remained undecided. Several key races were seen as too close to call.
Party dominance in Congress will be a crucial determinant of the policy-making outlook for the next president, whether it is Democrat Hillary Clinton or Republican Donald Trump.
Democrats picked up their first Senate seat from Republicans as Representative Tammy Duckworth, as expected, defeated Senator Mark Kirk in Illinois, according to the major TV networks.
Ms Duckworth is a double-amputee Iraq war veteran. With her victory, Democrats need to pick up four more seats from Republicans in order to win a majority in the Senate.
The networks projected that in Indiana, former Senator Evan Bayh failed in his bid to return to the Senate, losing to Republican Representative Todd Young.
The two candidates had been vying to replace Republican Dan Coats, who retired. Mr Bayh's loss was a missed opportunity for Democrats to gain a seat.
In Florida, incumbent Senator Marco Rubio, who ran unsuccessfully for the Republican presidential nomination earlier this year, was declared the winner and re-elected.
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