As well as talks with President Trump, Mrs May has met the premiers of China, Japan and India for one-to-one meetings during the two-day summit.
"We're in a dire situation right now", said Jenkins, adding that USAID was also concerned with the situation in southern Ethiopia.
President Trump said he looks forward to "a lot of very positive things happening, for Russian Federation and for the United States and for everybody concerned".
May is looking to secure a trade deal with the United States as Britain renegotiates its terms of trade with the European Union ahead of its withdrawal from the 28-nation bloc.
Nineteen of the 20 nations gathered in Hamburg, Germany for the G20 Summit have agreed to a joint statement on Saturday, which covers a range of issues, including global trade and the environment.
Trump said he anticipates an agreement on new trading arrangements with Britain to be a "very powerful" one that would work "great for both countries".
The US president hailed the "very special relationship" he had developed with May.
Trump sparked worldwide anger earlier in the year when he withdrew the US from the Paris Climate Accords.
Michel Barnier spells out Brexit consequences to UK
He went on, "In reality the " no deal " scenario would aggravate the lose/lose situation, which is a necessary effect of Brexit". The EU's chief Brexit negotiator, Michel Barnier.
Although leaders from both countries have said Trump plans to visit, doubts hover over Trump's first trip to Great Britain after reports that the president fears protests there.
The discussions with the US President come against a backdrop of tension though, as Trump's stance on trade and climate change - announcing he would withdraw the US from the Paris agreement last month - has proved tricky for other world leaders.
Queen Elizabeth then failed to mention Trump's visit in a speech to Parliament, an absence that raised eyebrows because she did mention an upcoming visit from the Spanish royal couple.
'We'll get there, ' Trump said, without explicitly promising a visit.
We've had tremendous talks, there is no country that could possibly be closer than our countries, and have been for a long time, and I just wanted to say thank youveryr much.
Merkel said: "The discussions are very hard, I don't want to talk around that".