Mrs May is holding early morning talks with Mr Trump in the margins of the gathering of world leaders which has been the target of protests in which nearly 200 police officers have been injured.
Trump also confirmed he will visit the British capital, though he did not say when, putting an end to speculation that the trip may have been quietly scuppered due to a backlash in Britain.
Asked when Mr Trump might visit, Mrs May said: "We don't have a date yet, we are still working on a date for when he will be making that visit".
"I think trade will be a very big factor between our two countries", he said.
After that, Trump will have two marathon talks with Indonesian President Joko Widodo and Singapore's Prime Minister Lee Hsien Loong.More news: Hundreds at Bronx Vigil Remember Slain NYPD Officer's Dedication
United States President Donald Trump left midway through a Saturday morning meeting at the weekend's Group of 20 summit, leaving eldest daughter Ivanka in his stead between British Prime Minister Theresa May and Chinese President Xi Jinping.
"We're in a dire situation right now", said Jenkins, adding that USAID was also concerned with the situation in southern Ethiopia.
The US president spoke of the "very special relationship" he has developed with Theresa May and said they had been working on a "very big" and "very powerful" deal.
Trump and May are sitting down for a meeting today while attending the G-20 summit of industrialized and developed nations.More news: Intense new 60-second 'Mini-Trailer' for Dunkirk
It acknowledges President Donald Trump's withdrawal from the Paris climate agreement without undermining the commitment of other countries.
The president additionally promised he would ink a "very powerful" bilateral trade deal with the United Kingdom.
While Trump's remarks could be popular in Poland and its right-wing government, they might have set him on a collision course with other allied leaders who view his actions and rhetoric as a far greater threat to Western values than immigration.
Confirming that the two countries are now working on an agreement, he said he would visit London in the near future.
Trump has clashed with other members of the G20 because of his America First trade agenda.More news: Cody Bellinger Walk-Off In 5-4 Over Royals
Putin, in a news conference Saturday, offered his version of events and said he thought Trump believed his in-person denials of Russian meddling.
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