At a political rally in Pennsylvania, Mr Trump told supporters he believed North Korea wanted to make peace.
But he said he might leave the talks quickly if it didn’t look like progress for nuclear disarmament could be made.
In his speech, the US leader warned of tariffs on European cars, and launched his slogan for re-election in 2020.
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What did he say about North Korea?
“Hey, who knows what’s going to happen?” said Mr Trump on Saturday at the rally for a Republican congressional candidate. “I may leave fast or we may sit down and make the greatest deal for the world.”
In his wide-ranging speech, he said he hoped a deal to ease nuclear tensions would happen, particularly to help countries like North Korea.
He also said he believed the North Koreans would honour their commitment not to test any more missiles. Mr Trump told the crowd: “I think they want to make peace, I think it’s time.”
Where could the talks be held?
No date or place has been set for the meeting, despite initial reports it would happen by the end of May.
South Korea’s presidential office said the North Korean truce village of Panmunjom, which sits at the demilitarised zone between the North and the South, was a “serious” option, Yonhap news agency reported.
Sweden, Switzerland and China have also been named as possible hosts.
No sitting US president has ever met a North Korean leader and Mr Trump’s decision to accept an invitation from the North Korean leader – relayed by South Korean envoys on Thursday – reportedly took top administration officials by surprise.
Mr Trump tweeted that a deal was “very much in the making”, though the White House said the meeting would not take place unless Pyongyang took “concrete actions”.
The US has made “zero concessions” with its sanctions, said Vice-President Mike Pence, following news of the upcoming meeting being agreed. He said he believed North Korea’s willingness to talk proved the US strategy of isolating the country was working.
Trump unveiled his 2020 election slogan
This was a speech meant for Mr Trump’s core supporters, the BBC Washington correspondent Chris Buckler says.
The president was supporting a Republican bid for a seat in congress but the packed out rally looked and felt like the start of the presidential campaign, our correspondent adds.
He announced that his 2020 re-election campaign slogan would be: “Keep America Great, exclamation point.”
Appealing to his base, he again raised the possibility of the death penalty for drug dealers.
President Trump talked tough on trade, describing tariffs as his baby.
He re-iterated his threat to tax cars imported from the European Union, saying that the EU better raise barriers and get rid of its own tariffs.
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“If you’re not going to do that, we’re going to tax Mercedes Benz, we’re going to tax BMW,” he said.
Mr Trump’s words may raise concerns or rile up anger overseas, our correspondent says, but it appealed to the audience Mr Trump wanted to address – his core supporters.
“For years the United States has been getting dumped on,” said one supporter at the rally. “Donald Trump is the master of the art of the deal.”