The visit by Kim Yong-chol comes as top diplomats from the two countries try to revive a cancelled summit between Trump and Kim, which was due to be held in Singapore on June 12.
Earlier the North Korean official, one of Kim’s most senior aides, met US Secretary of State Mike Pompeo, who said “good progress” had been made in talks to salvage the summit.
The US is hoping that Pyongyang will give up its nuclear weapons and permanently end its programme to produce more.
Following Pompeo’s meeting with Kim Yong-chol in New York on Thursday, the top US diplomat reiterated the US demand for a “complete, verifiable and irreversible denuclearisation” of the Korean Peninsula.
“Our two countries face a pivotal moment in our relationship, in which it could be nothing short of tragic to let this opportunity go to waste,” he said.
Kim Yong-chol is the most senior official from Pyongyang to visit the US in 18 years.
Trump cancelled the planned summit after accusing the North Koreans of “tremendous anger and open hostility”, but has since reiterated his openness to meeting Kim.
The US president said even if the meeting does go ahead, reaching a conclusive agreement may require more than one round of negotiations.
“I’d like to see it done in one meeting,” Trump told the Reuters news agency.
“But often times that’s not the way deals work. There’s a very good chance that it won’t be done in one meeting, or two meetings, or three meetings. But it’ll get done at some point.”
Kim Yong-chol’s visit to the US coincides with a visit by Russia’s foreign minister, Sergey Lavrov, to North Korea, where he met Kim Jong-un.
The North Korean leader said his country’s commitment to denuclearisation remained “unchanged, consistent, and fixed”.
He added that he hoped the denuclearisation of the Korean Peninsula and the mending of relations with the US, would be dealt with on a “stage-by-stage” basis.
A Russian foreign ministry statement said that Lavrov had invited Kim to visit Moscow.
The current diplomatic wrangle to denuclearise the region cuts a sharp contrast to the war of words between the US and North Korean leaders over the last few years.
Trump referred to Kim Jong-un dismissively as “rocket man” and warned that the US could “totally destroy” North Korea.
For its part, Pyongyang has called Trump a “dotard”.
Trump has since referred to the North Korean leader as “very open” and “very honourable”.
The thaw in relations between the decades-old rivals comes in tandem with improving relations between North and South Korea.
In April, Kim and South Korean President Moon Jae-in pledged to sign a peace treaty later this year to officially halt the Korean War during a landmark meeting in the border village of Panmunjom.
On Friday, senior officials from the two states met again at the village in the demilitarised zone that separates North Korea from South Korea.
The two sides proposed to establish a joint liaison office in the North Korean border city of Kaesong, where the two Koreas operated a factory park together until its closure in 2016.