Prime Minister Theresa May has lobbied Donald Trump over the importance of preserving jobs at aerospace giant Bombardier in Northern Ireland, as the pair met for talks in New York.
And Mrs May pressed the US president over the importance of the international nuclear deal with Iran, which Mr Trump has threatened to tear up.
During the 30-minute talks on the margin of the United Nations General Assembly, Mr Trump assured the Prime Minister of the USA's desire for a strong trading relationship with the UK, including a trade deal once Britain leaves the EU, said a Downing Street source.
Seated in front of a row of US and UK flags as the pair shook hands, the president said: "We will be doing a lot of trading with the United Kingdom and we look forward to it.
"We've gotten to know each other over the last period of a year and it's a real honour to have you here."
Downing Street said the Prime Minister reiterated the importance of Bombardier to the economy of Northern Ireland and the priority she placed on protecting the jobs the company provides.
A preliminary ruling is expected from US trading authorities within days on a complaint from Boeing alleging unfair dumping on the American market of the Canadian firm's C-Series jets, whose wings are made in Belfast.
Mrs May also discussed Bombardier with Canada's PM Justin Trudeau during a visit to Ottawa on Monday.
It is understood she was pressed to raise the issue by DUP leader Arlene Foster, whose 10 MPs are propping up her minority administration in the House of Commons.
Mrs May reaffirmed the UK's strong commitment to the nuclear deal with Iran, telling the president it was vitally important for regional security and should be carefully monitored and properly enforced, said Downing Street.
The pair also discussed the need to counter destabilising Iranian activity in the region.
Mrs May and Mr Trump agreed that North Korea's missile tests were conducted "against all standards of international behaviour" and that it was vital for the international community, including China, to come together to exert maximum economic pressure on the regime, said Number 10.
The bilateral meeting at the Lotte Palace Hotel in Manhattan began half an hour late after Mrs May's keynote address to the UN was delayed because previous speakers overran.