Mr Trump's cancellation of his trip has raised questions in Britain over the links between Washington and its closest traditional ally in Europe, widely called the "special relationship".
More than a year into his presidency, Mr Trump has yet to visit London and many British voters have promised to protest against a man they see as crude, volatile and opposed to their values on a range of issues.
Mr Tillerson, a former Exxon Mobil CEO, met British Prime Minister Theresa May in her Downing Street residence and then held talks with Foreign Secretary Boris Johnson.
"We treasure this relationship, and I treasure Boris's relationship with me personally and the work that we do together on these many issues," Mr Tillerson told reporters.
"Sometimes we forget about the importance of our own relationship," he said. "We need to pay attention to that relationship and the importance of this relationship on a bilateral basis as well."
A pillar of Britain's foreign policy for a century, the special relationship with Washington has taken on added importance as Britain prepares to leave the European Union in 2019.
Mrs May and Mr Tillerson discussed "continuing depth and breadth" of the special relationship, the PM’s office said.
They also touched on one of their most pressing diplomatic challenges: disagreement over the future of a landmark international deal to curb Iran's nuclear ambitions. The deal has been cast into doubt by Mr Trump, but Britain, along with France and Germany, wants to keep it.
While in London, Mr Tillerson visited the new $1 billion US embassy. Mr Trump earlier this month criticised the move to new diplomatic premises as part of a bad deal agreed by the administration of Barack Obama.
Trump cancelled a trip to Britain to open the new embassy, saying he did not want to endorse a bad deal agreed by the Obama administration to sell the old one for "peanuts".
Mr Tillerson was greeted by US Ambassador Woody Johnson as workers finished planting shrubs in the grounds of the new embassy. America's top diplomat then met some of the marines who are stationed at the embassy.
Asked when there would be a ribbon cutting ceremony, Ambassador Johnson said: "At some point we're going to do it, but there's no urgency to that. We'll do it when the time is right."
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