Boris Johnson and US Vice President-elect Mike Pence have spoken by phone about the US’s “close relationship” with the UK.
The UK foreign secretary said on Twitter they had agreed on the “importance of the special relationship and need to tackle global challenges”.
Sources close to Mr Johnson said the two men spoke for 10 minutes on Thursday.
The BBC understands it was Mr Pence’s first call to an overseas politician.
On Thursday, Mr Johnson said critics of Donald Trump’s victory should end the “collective whinge-o-rama” and be positive about the possibilities.
After Mr Johnson’s comments, Mr Pence responded: “Just spoke to @Boris Johnson. Discussed America’s longstanding and close relationship with the UK.”
BBC diplomatic correspondent James Landale noted that the US vice president-elect had opted not to use the phrase “special relationship”.
‘Hugely irritated’
Mr Johnson, who last year suggested that Mr Trump had been “out of his mind” for suggesting a ban on Muslims entering the US, has insisted the UK should be optimistic about the future following Mr Trump’s victory.
At a news conference on Thursday, before speaking to Mr Pence, he said it was time to be “overwhelmingly positive about the possibilities” of a Trump presidency and described the US president-elect as a “deal maker”.
“I believe that this is a great opportunity for us in the UK to build on that relationship with America that is of fundamental economic importance to us, but also, great importance for the stability and prosperity of the world,” Mr Johnson said.
“I would respectfully say to my beloved European friends and colleagues that it’s time that we snapped out of the general doom and gloom about the result of this election and collective whinge-o-rama that seems to be going on in some places.”
‘Quite dangerous’
But former MI6 chief Sir John Sawers told BBC Radio 4’s World at One: “I don’t think Donald Trump quite yet knows what the pressures will be on him when he becomes president.
“We’ve seen that when he feels slighted, when he feels criticised, he reacts quite fiercely. If you translate that into global affairs it could have consequences which are dangerous for everyone.”
Sir John said one of the failures of President Obama’s administration had been managing relations with Russia: “We’re getting back into a world which is quite dangerous, and I think that is the biggest threat.”
Meanwhile Downing Street has rejected claims that ministers will be forced to use Nigel Farage as a “go-between” with the Trump administration.
The Daily Telegraph reported ministers would have to seek the advice of UKIP’s interim leader because they have no links to the president-elect.
But sources close to the prime minister told the BBC that Mr Trump, who defeated Democratic Party candidate Hillary Clinton, favoured a relationship with Theresa May as close as that of former UK and US leaders Margaret Thatcher and Ronald Reagan in the 1980s.
Mr Trump invited Mrs May to visit Washington, during a phone call on Thursday in which both stressed the importance of UK-US relations.
BBC political correspondent Iain Watson says Downing Street has been “hugely irritated” with the claim ministers were seeking the services of Mr Farage in forging links with the Trump administration.
A source close to Mr Farage made it clear that he had no intention of working with Conservative ministers.
