The UK government did not take its "eye off the ball" over the seizure of a UK-flagged oil tanker in the Gulf on Friday, the chancellor told the BBC.
Philip Hammond said the UK has been working closely with US and European partners in response to Iran's actions.
But ex-Tory party leader Iain Duncan Smith said the Stena Impero's capture was a "major failure" for the UK.
Theresa May is to chair a meeting of the emergency response committee Cobra on Monday to discuss the issue.
Iran's foreign minister has said that only "prudence and foresight" would reduce tensions between Iran and Britain.
The 23 crew members, who are Indian, Russian, Latvian and Filipino, have now been taken off the ship for "questioning", Iran's Press TV has reported.
Charts showing the ship was in Omani waters when it was captured prove its seizure was in "clear violation of international law", the UK Chamber of Shipping said.
The UK has accused Iran of "unacceptable and highly escalatory" action, in a letter to the president of the United Nations Security Council.
What have UK politicians said?
Speaking on the BBC's Andrew Marr programme, Mr Hammond said the UK would pursue "every possible diplomatic route" to resolve the situation.
He said sanctions, including financial, against Iran are already in place, and it was unclear what more could be done.
Mr Hammond, who announced his intention to resign if Boris Johnson becomes prime minister, added: "We are of course looking at all the options."
But Mr Duncan Smith told the BBC there are questions to be raised about the British government's behaviour.
He said the detention of a tanker carrying Iranian oil two weeks earlier ought to have served as a warning British vessels in the Gulf needed protection.
The MP said he understood the US had offered the UK "assets" to support its shipping and they were not taken up.
"This is a major failure and the government has to answer that charge very quickly indeed."
Defence minister Tobias Ellwood told Sky the Royal Navy was too small to manage the UK's interests around the globe but had not been negligent in protecting its ships.
Foreign Secretary Jeremy Hunt earlier said Iran viewed this as a "tit-for-tat situation" but "nothing could be further from the truth".
Labour shadow justice minister Richard Burgon said the UK should avoid becoming Donald Trump's "sidekicks" and warned a US-backed conflict with Iran could be worse than the Iraq War.
On Friday, the Stena Impero was seized by the Iranian Revolutionary Guard in the Strait of Hormuz after Tehran said it was "violating international maritime rules".
A second tanker, the British-owned MV Mesdar, was also boarded by armed guards but released.
Video released by Iran's Revolutionary Guard-affiliated Fars news agency appeared to show the moment the tanker was raided.
HMS Montrose was alerted but it was too far away to stop the seizure.
A recording of radio exchanges between a Royal Navy frigate and Iranian armed forces vessels moments before the tanker was seized was also released.
In the recording, an Iranian vessel tells HMS Montrose it wants to inspect the Stena Impero for security reasons.
Iran's state-run IRNA news agency said the tanker was captured after it collided with a fishing boat and failed to respond to calls from the smaller craft.
But Mr Hunt said it was seized in Omani waters in "clear contravention of international law" and forced to sail into Bandar Abbas port in Iran.
The tanker's owner, Stena Bulk, said it has made a formal request to visit the crew members.
A relative of an Indian crew member aboard the Stena Impero told the BBC on Sunday the family was concerned and had not received any messages from him since the vessel was detained.
The seizure of the Stena Impero comes two weeks after Royal Marines helped seize Iranian tanker Grace 1 off Gibraltar, because of evidence it was carrying oil to Syria in breach of EU sanctions.
Mr Hunt said the Grace 1 was detained legally, but Iran said this was "piracy" and threatened to seize a British oil tanker in retaliation
What has Iran said?
Iran's foreign minister Javad Zarif tweeted that the UK "must cease being an accessory to #EconomicTerrorism of the US".
He said Iran guarantees the security of the Gulf and the Strait of Hormuz, and insisted its action were to "uphold international maritime rules".
Iran's ambassador to London has warned the UK against escalating tensions.
Hamid Baeidinejad said in a tweet: "This is quite dangerous and unwise at a sensitive time in the region. Iran however is firm and ready for different scenarios."
What's the background to tensions in the Gulf?
Relations have been deteriorating between Iran and the UK and US.
In April, the US tightened sanctions it had re-imposed on Iran after withdrawing from a 2015 nuclear deal.
The US blamed Iran for attacks on tankers since May, which Tehran denies. On Friday, the US claimed to have destroyed an Iranian drone in the Gulf.
The UK government has remained committed to the deal, which curbs Iran's nuclear activities in return for the lifting of sanctions.
However, the UK's help in seizing the Iranian tanker Grace 1 infuriated Iran.
Last week, the UK said Iranian boats also attempted to impede a British oil tanker in the region before being warned off by HMS Montrose but Iran denied this.
The White House said Friday's incident was the second time in more than a week the UK had been "the target of escalatory violence" by Iran.
US Central Command said it was developing a multinational maritime effort in response to the situation.
The Pentagon said US troops are being deployed to Saudi Arabia to defend American interests in the region from "emergent credible threats".
France and Germany called on Iran to release the Stena Impero.
Diplomatic solution 'will be complicated'
A diplomatic solution to this crisis is going to be complicated, not least because Britain's relationships with its traditional partners - the US and the Europeans - are under strain.
Diplomatic pressure - action at the UN or tough economic sanctions - requires the building of a coalition.
Think back to the collective action taken against Moscow in the wake of the murder of a British woman by Russian agents in Salisbury.
The US and Britain's Nato and European allies all expelled Russian diplomats in an impressive show of solidarity.
But will the same solidarity be shown towards Tehran?
France and Germany have given London rhetorical support. President Trump is standing beside his British ally.
But the US and the EU are fundamentally at loggerheads over the fate of the nuclear deal with Iran and what many European capitals see as a thinly disguised US policy that seeks regime change in Tehran.
How 'British' is the tanker?
Ships must fly the flag of a nation state but it does not need to be the same nation as its owners.
The Stena Impero is Swedish-owned and those on board are Indian, Russian, Latvian and Filipino.
A relative of a crew member from India, who did not want to be identified, told the BBC the family was being kept well informed by the Swedish company.
They felt reassured about diplomatic efforts to free the ship after a meeting with company officials attended by crew members' families on Sunday afternoon, he said.
But it is the UK flag that is important symbolically and politically, explained Richard Meade from maritime publication Lloyds List.
"Historically speaking it means that the UK owes protection to the vessel."