The top White House diplomatic envoy – flying in days after the US President cancelled a trip to London scheduled for next month – held talks with Theresa May and Boris Jonnson yesterday.
And he used the visit to play down suggestions of cooling relations between Downing Street and the White House.
Following his meetings, Mr Tillerson insisted the link between the UK and the US was still viewed as the “special relationship”, adding: “It has been and will be.”
He said: “We spend a lot of time talking about the world’s problems – sometimes we forget about the importance of our own relationship.
“We treasure this relationship.
“I treasure Boris’s relationship with me personally.”
He added: “It is always worth saying that the relationship between the US and the UK is absolutely fundamental to our diplomacy but also to our economy.”
President Trump was due to visit London to oversee the official opening of a new US Embassy building.
He triggered surprise by scrapping the visit, saying he did not want to open the building commissioned by his predecessor Barack Obama.
The cancellation followed warnings of mass anti-Trump demonstrations in London and a spat between Downing Street and the White House about the President retweeting a video posted by the extremist Britain First group.
Mrs May is expected to meet Mr Trump at the World Economic Forum in Davos later this week.
But the meeting appeared to be in doubt yesterday following speculation that a political crisis in Washington could scupper the president’s travel plans.
Mr Tillerson discussed foreign policy concerns about Iran, Turkey and the Yemen with his hosts yesterday.
A Downing Street spokesman said: “The Prime Minister attended a part of the National Security Adviser’s meeting with the US Secretary of State Rex Tillerson at 10 Downing Street today.
“They discussed the continuing depth and breadth of the special relationship.
“They agreed on the importance of the international community coming together to counter Iran’s destabilising regional activity, and the Prime Minister reiterated the UK’s commitment to the Iran nuclear deal.”