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".
He has confirmed he will visit London, without specifying when.
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 worldwide trade and the environment.
In their June 2016 referendum, the majority of the British citizens voted in favor of Brexit (51.9% to 48.1%).
Theresa May is discussing her ambitions for post-Brexit trade deals with the United States and Japan on the final day of the G20 summit, as leaders battle through "very difficult" talks.
As he met with British Prime Minister Theresa May at the G20 summit in Germany, Trump predicted that trade would be "a very big factor" between the two nations.
Trump also said he will visit London soon.
Later, Trump met with Indonesian President Joko Widodo - who seemed intent on getting him to commit to a Jakarta visit during his presidency.
May was the first foreign leader to visit Trump at the White House after the inauguration.
When asked about timing, he responded: "We'll work that out".
Before the meeting at the G20 summit, Donald Trump stated that the United Kingdom and US have a very special relationship.
May also said she was optimistic about hoped-for future trade pacts with the USA and other countries after meeting Trump at the Group of 20 summit.
And as Britain prepares to leave the European Union, Trump promised that "a very powerful deal" on trade would be reached "very very quickly" as a result of their talks. The US will want to know what access its companies and banks in Britain will have to the rest of the EU.
As well as discussions on a future trade deal with the US, May raised Trump's controversial decision to pull out of the global Paris agreement on tackling climate change.
"I will be making that message". "I can get into serious trouble if I don't bring back some good news for your millions of fans in Indonesia", he said.