The meeting, on the sidelines of the United Nations General Assembly in New York, came after two phone calls between the leaders since Burnham took office in July, China Daily reported.
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Burnham told reporters he and Trump had “found a connection” during those conversations, which he described as warm and cordial.
According to Reuters, Burnham wanted to press British interests even where they differed from Trump’s, but without antagonizing the US president. Trump offered no opposition when Burnham briefed him ahead of the UK’s announcement, earlier this month, of sanctions on imports from illegal Israeli settlements in the occupied West Bank.
The two leaders’ talks were expected to cover ceasefire efforts for the Russia-Ukraine conflict, the Middle East, defense spending, trade, and artificial intelligence.
Burnham’s past criticism of Trump was downplayed by one UK minister on Sunday as “politics” and not a barrier to cooperation, with officials stressing defense ties, intelligence-sharing, and Ukraine as priorities.
The UK leader also hailed the deal between Denmark, Greenland, and the US to “strengthen security in the Arctic”, and said he would pass on congratulations to Trump as part of efforts to keep the wider relationship positive.
In his address to the UN General Assembly on Tuesday evening, Burnham said he planned to strike a note of “hope” while warning of “dark clouds of instability” facing the world, the Associated Press reported.
The prime minister said he would use the speech to focus on artificial intelligence, arguing nations could be “clear-eyed” about both its benefits and risks.
While traveling to New York, Burnham announced limited UK military support for Saudi Arabia, including the deployment of a Royal Air Force tanker aircraft to refuel Saudi jets involved in defensive operations against Houthi missile attacks from Yemen. Burnham said the decision was about “acting to secure the interests of Britain and the wider region”.
The meeting of the two leaders followed a turbulent week after Trump told reporters on his visit to Dublin, Ireland on Sept 12-13 that he would “love” to see a united Ireland and predicted unification would “happen eventually”.
Downing Street reiterated that Burnham’s position on Northern Ireland remained unchanged and that the conditions for a border poll under the 1998 Good Friday Agreement had not been met.
Kemi Badenoch, leader of the UK’s opposition Conservative Party, accused Trump of “inflaming tensions” in Northern Ireland and called his comments “deeply unhelpful”.
Gavin Robinson, leader of the Democratic Unionist Party in Northern Ireland, said the region’s future would be “decided by the people of Northern Ireland, not by commentary in London, Dublin, or Washington”.
