The Prime Minister and the US president also talked about the civil war in Yemen and the importance of a swift post-Brexit trans-Atlantic trade deal.
Mrs May spoke to the American president after Britain joined 13 other members of the United Nation’s Security Council in backing a resolution, vetoed by the US, which rejected the recognition of Jerusalem as the capital of Israel.
A Downing Street spokesman said: “They discussed the different positions we took on the recognition of Jerusalem as the Israeli capital, and agreed on the importance of the US bringing forward new proposals for peace and the international community supporting these efforts.
“The Prime Minister also raised Yemen, highlighting our ongoing deep concerns at the humanitarian situation. They agreed on the vital importance of reopening humanitarian and commercial access to prevent famine and alleviate the suffering of innocent Yemenis.
“The Prime Minister updated the president on the recent good progress of the Brexit negotiations, and the president set out the progress he had made on his economic agenda. They agreed on the importance of a swift post-Brexit bilateral trade deal.
“They wished each other a very merry Christmas and looked forward to keeping in close touch.”
Mrs May also offered her condolences to the president for the loss of life in a train crash in Washington state this week.
Mr Trump sparked protests across the Middle East by breaking with decades of US neutrality in the peace process on December 6 to announce he recognised Jerusalem as Israel’s capital and would move the US embassy from Tel Aviv.
Mrs May said at Prime Minister’s Questions that day she intended to talk to Mr Trump about the matter, but this is the first time they have spoken.
The PM’s spokesman said the fact it took 13 days between Mrs May announcing her intention to speak with Mr Trump about Jerusalem and the call actually taking place was a “matter of scheduling” and the PM “didn’t put any timeframe on it”.
It is also the first time the pair have talked since their extraordinary transatlantic row over Mr Trump’s sharing of inflammatory anti-Muslim videos posted by the far-right Britain First group’s deputy leader, Jayda Fransen.
At the time, the PM said Mr Trump was “wrong” to retweet the videos, and the US president hit back at Mrs May on Twitter by telling her to focus on “destructive radical Islamic terrorism” in the UK, rather than on him