Hours before their discussion on Sunday, Mr Trump had applauded Sir Keir for his “very good job thus far” and shared that the pair had a “very good relationship”.
Prior to his inauguration, a Hamas official said that Mr Trump had informed mediators that he desired an agreement, the BBC has revealed.
The phone call between Sir Keir and Mr Trump lasted 45 minutes and, according to Downing Street, the pair “discussed the importance of working together for security in the Middle East”.
During the conversation, Sir Keir also explained how his government was “deregulating to boost growth”.
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There is no bad blood between Sir Keir and Mr Trump right now. The two men have already met several times, including when Sir Keir visited Trump Tower in New York during the presidential campaign.
In an interview with the BBC on Saturday, Mr Trump praised the prime minister’s leadership, saying he was a “very good guy”.
He added: “I may not agree with his philosophy, but I have a very good relationship with him.”
Following his conversation with Mr Trump, Sir Keir posted on X, saying, “I spoke with @POTUS today and congratulated him on his inauguration.
A few days prior to Mr Trump’s inauguration, Sir Keir told the Financial Times that Mr Trump “came to New York to have dinner with me and I was very grateful for that”.
“Our ambition is to have a deal of some sorts with the US, a trade deal. That’s where our focus is,” adding that the “US is our closest ally”.
He said: “I think that when you look at past prime ministers, it’s taken between a week or up to a month to come to Washington.
“The importance is the strength of the relationship and the serious discussions that we have.
“In the end, we have war in Europe, we have a ceasefire in the Middle East, but it’s incredibly fragile, and there are important malign actors like Iran that we’ve got to discuss with the United States and, of course, our growing trade relations with the United States.”