Tillerson said Monday while traveling in Europe that the US recognizes Turkey's "legitimate right" to defend itself from terrorists. "A team that will meet with counterparts", Xinhua quoted Tillerson, who was en route to France, as saying.
US President Donald Trump has repeatedly criticized the deal and Iran's compliance with it.
Iran has condemned the European strategy of giving in to some U.S. demands while attempting to save the whole nuclear deal.
"The embassy actually, is gonna really work", British Foreign Secretary Boris Johnson said ahead of Tillerson's arrival.
"We spend a lot of time talking about the world's problems - sometimes we forget about the importance of our own relationship", he said, adding: "We need to pay attention to that relationship and the importance of this relationship on a bilateral basis as well". Following his meeting with Boris Johnson, he told reporters that the "special relationship" between the U.S. and United Kingdom would endure.
Mr Tillerson said "flaws" in the deal could be fixed by working groups and a possible "side agreement".
The US embassy had been in Grosvenor Square since 1938.
More than a year into his presidency, 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. "We treasure this relationship".
Secretary of State Rex Tillerson has become the highest-ranking USA official to visit the new American embassy in London, a building that President Donald Trump derided for its cost and location.
U.S. Secretary of State Rex Tillerson is due to arrive in London later on January 21 on the first leg of a weeklong trip to Europe that will also take him to Paris, Warsaw, and the World Economic Forum in Davos, Switzerland.
Asked when there would be a ribbon cutting ceremony, Johnson said: "At some point we're going to do it, but there's no urgency to that".
But despite the President's snub, the US Secretary of State Mr Tillerson visted the site this morning. "I treasure Boris' relationship with me personally", he said.
May's office said in a statement that she attended part of a security meeting with Tillerson.
"They discussed the continuing depth and breadth of the special relationship", a spokesperson said.
"They agreed on the importance of the global community coming together to counter Iran's destabilizing regional activity, and the prime minister reiterated the U.K.'s commitment to the Iran nuclear deal".