Raab, making his first visit to the US since assuming office last month, said he had a “preliminary chat” with the president on Tuesday covering a range of issues from security to trade.
He said Trump had been “effusive in his warmth” towards Britain and had expressed his “high regard” for Boris Johnson as Prime Minister.
The decision to invite Raab into the Oval Office for an unscheduled meeting will be seen as a sign the president is keen to repair relations with the UK after they soured in the dying days of Theresa May’s premiership.
It comes after the Obama-era former director of the US National Economic Council said it would be “delusional” for the UK to expect a preferential trade deal with the US after Brexit.
Raab, who was in the White House to meet Vice President Mike Pence, said: “He called me into the Oval Office. He was effusive in his warmth for the United Kingdom.
“It’s amazing to hear an American president talk about our country in such warm terms. He expressed his high regard for Boris Johnson as a Prime Minister.
“We talked about all the things that we want to do together in the post-Brexit vision for the UK, whether it’s getting a free trade deal done and there’s obviously going to be a lot of work to make that happen. There’s a huge appetite on both sides to achieve that.
“And then all the range of security issues that we share in common and want to make sure we strengthen the relationship and build our capacity to tackle those issues together.”
On Tuesday, Larry Summers, who served under President Barack Obama, said Britain would have “no leverage” in trade talks.
“I’m not sure what Britain wants from the United States that it can plausibly imagine the United States will give,” he told BBC Radio 4′s Today programme.
Trump’s relationship with May ended acrimoniously following the leak of diplomatic cables from the British ambassador to the US, Sir Kim Darroch, which were highly critical of his administration.
Sir Kim felt compelled to stand down after Trump made clear the White House would no longer deal with him and Johnson – at that stage the Tory leadership favourite – failed to offer him his unequivocal support.
The president also bitterly criticised May’s handling of the Brexit negotiations, accusing her of ignoring his advice.
Raab’s visit to the White House came at the start of the second leg of a three-day visit to North America intended to “fire up” trade with Britain’s non-EU partners.
After meeting Canadian foreign minister Chrystia Freeland in Toronto on Tuesday, he is due to travel to Mexico for further talks on Thursday.