A sense of crisis in the world's busiest oil shipping lane has been building up for weeks as Iran responds to US President Donald Trump's "maximum pressure" campaign.

The US economic sanctions and stepped-up military presence are designed to force Iran to renegotiate a landmark 2015 nuclear pact from which Trump pulled out last year.

Britain further outraged Iran by seizing one of its tankers -- the Grace 1 -- on July 4 on suspicion of it carrying oil to Syria in violation of EU sanctions.

Iran vowed to retaliate and its Revolutionary Guards stormed and detained the UK-flagged Stena Impero and its 23 crew as they sailed through the Strait of Hormuz on July 20.

New British Foreign Secretary Dominic Raab flatly rejected the idea of the two tankers being exchanged or simultaneously released in a bid to dial back the tensions.

"There is no quid pro quo," Raab told BBC radio.

"This is not about some kind of barter. This is about international law and the rules of the international legal system being upheld," he said.

"That is what we will insist on."

Iranian President Hassan Rouhani had hinted earlier that he was open to a tanker swap.

- 'Geopolitical tussle' -

Iran said on Sunday that its ship's seizure was also a violation of the 2015 nuclear pact that Britain co-signed and is trying to keep alive with EU allies.

Its remaining participants met in Vienna over the weekend for heated talks that also saw Iran lash out at Britain's proposal for European nations to lead a naval and air Gulf escort mission.

Britain's HMS Montrose frigate began helping UK-flagged tankers enter into and out of the Gulf last week.

Its naval presence near Iran grew to two with the arrival on Sunday of the HMS Duncan destroyer -- the most advanced warship Britain currently has.

The UK defence ministry said the two will conduct escorts together for the next month.

The Montrose will then go in for scheduled maintenance and be replaced by the HMS Kent frigate later this year.

"Freedom of navigation in the Strait of Hormuz is vital not just to the UK, but also our international partners and allies," UK Defence Secretary Ben Wallace said.

Yet Britain's European force proposal is running up one already being prepared by the United States.

Both plans have strongly angered Tehran.

Iranian government spokesman Ali Rabiei said on Sunday that the proposed European fleet "carries a hostile message, is provocative and will increase tensions".

Britain's Raab said London was still insisting on a European force -- despite the potential conflict with Washington.

"This shouldn't be some sort of geopolitical, EU versus US tussle," he said in the radio interview.

"It should be (about) what puts us in the best position with the widest group of international actors to uphold the rule of law."

He added that "it would be important for the European-led initiative to have US support to make it viable".

European nations have responded to Britain's proposal with caution.