Britain's allies have called for the release of the vessel, warning of the danger of escalation.
US President Donald Trump said he would hold talks with Britain about the tanker's seizure by Iran's Revolutionary Guards.
"And this only goes to show what I'm saying about Iran: trouble. Nothing but trouble," he told reporters at the White House on Friday.
He again denounced the 2015 deal between Iran and Western powers aimed at curbing Tehran's nuclear ambitions, describing it as a "ridiculous agreement" made by his predecessor Barack Obama.
Trump pulled the United States out of the deal last year and began ratcheting up sanctions against Iran.
British Foreign Secretary Jeremy Hunt said Tehran's seizure of the tanker showed "worrying signs Iran may be choosing a dangerous path of illegal and destabilising behaviour".
The incident came hours after a court in the British territory of Gibraltar extended the detention of an Iranian tanker seized two weeks ago on allegations of breaching EU sanctions against Syria.
"Our reaction will be considered but robust. We have been trying to find a way to resolve Grace 1 issue but WILL ensure the safety of our shipping," Hunt said on Twitter.
British cabinet minister James Brokenshire said London was still seeking to establish diplomatic connections with Tehran over the incident.
"The action of the Iranians is completely unacceptable. It is so important that we maintain this free navigation through the Gulf," he told BBC radio.
"We want to see this matter resolved in a diplomatic way." - Germany called on Iran to immediately release the Swedish-owned, British-flagged Stena Impero.
The seizure was a "dangerous further aggravation of an already tense situation," a foreign ministry statement said.
France made a similar call, with the foreign ministry saying Iran's action "hampers a necessary de-escalation of tensions in the Gulf region".
"We call on Iranian authorities to quickly release the ship and its crew, and to respect freedom of navigation principles in the Gulf."