Aides for both parties also used the meeting to discuss a future Trump visit to the United Kingdom, which is now expected to take place sometime in the second half of 2018, according to United Kingdom officials.
Trump guestured to May and said: "We will talk about it".
Speaking during a photo opportunity, Mr Trump said the United States and UK are "very much joined at the hip".
On Friday, Trump is expected to meet with Paul Kagame, President of Rwanda and current Chairman of the African Union, "to reaffirm the US-Africa relationship and to discuss shared priorities including trade and security".
So the Power Africa project survives, but only just if the White House lack of enthusiasm is anything to go by.
Trump said "it's an honor to be with Prime Minister May, and we've had a great discussion".
However, he confessed that although he does not expect any progress at the meetings with other world or entrepreneurial leaders, Trump's interactions in Davos may provide a notion of the limits of USA unilateralism.
Khan, a Muslim, called Britain First, the far-right party that Trump retweeted, "a vile, extremist group that exists exclusively to sow division and hatred in our country". We're working on transactions in terms of economic development, trade, maybe most importantly, military.
"And we look forward to that and we are starting that process pretty much as we speak", he added.
He also said that "we are very much joined at the hip when it comes to the military" adding that the United States was ready "to fight for you" [the UK].
"The two leaders reiterated their desire for a strong trading relationship post-Brexit, which would be in the interests of both countries", her office said.
"I can tell you, Israel does want to make peace, and they [the Palestinians] are going to have to want to make peace, too, or we aren't going to have anything to do with them any longer", he continued, as he sat next to Prime Minister Benjamin Netanyahu.
"[We stand] shoulder to shoulder because we are facing the same challenges across the world".
Trump had been expected to travel to London earlier this month for the grand opening of a new, state-of-the-art U.S. embassy here.
However, Trump warned that the world "cannot have free and open trade if some countries exploit the system".
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