Iran's ambassador to London has said Britain should respond "in a positive way" to the release of the 15 Royal Navy personnel held for 13 days.
The naval crew have shared their experiences with the media
Rasoul Movahedian said that Iran wanted help to release five Iranians held by the US in Iraq, and to ease fears over its nuclear programme.
He told the Financial Times: "If [the British] want to be helpful and use their influence we will welcome that."
The crew have two weeks' compassionate leave to spend with their families.
Iran has said a press conference where the crew described being bound and held alone was "theatrical propaganda" that did not justify their "mistake".
Mr Movahedian told the FT: "We played our part and we showed our good will... now it is up to the British government to proceed in a positive way," he said.
He denied that the release of the crew was linked to the case of the Iranians being detained in Iraq or any other case.
But he added: "We will welcome in general any steps that could defuse tensions in the region."
The ambassador also suggested the resolution of the dispute should be used as an opportunity to open up a dialogue between Iran and the UK.
"We share in the British people's happiness and we believe it is the right time for the British government to affirm its willingness to establish sensible lines of communication with Iran," he said.
The BBC's Jill McGivering told BBC Radio 4's Today programme that some analysts believed "a face-saving compromise was worked out after Britain and Iran opened up a new, high level and direct channel of communication".
'Key' US role
She added: "That has led to debate about whether a similar approach could also be applied to larger disputes with Iran from the nuclear issue to its involvement in Iraq."
However, our correspondent argued that "the key" to Western links with Iran depended on "how the US feels".
Sir Christopher Meyer, a former British ambassador to the US, said the outcome of the dispute meant that "Iran's standing in the Muslim world...will have been raised".
He said the capture of the sailors had resulted in "humiliation" for the UK.
Similarly, former Iranian diplomat Mehdi Varzi said the dispute was used by Tehran "to show the Arab world these British sailors were just normal people and could be taken at will", therefore undermining the image of western military strength in the region.
He added that Tehran had used the situation to "project a slightly softer image".
Mr Varzi said Iran wanted to show that "if somebody comes to negotiate with them they are reasonable people".
On Friday, at the Royal Marines Barracks at Chivenor, Devon, the crew said they were told by their captors that if they did not admit they were in Iranian waters when captured they faced seven years in prison.
The officer in charge, Lieutenant Felix Carman, 26, of Swansea, said the sailors and marines were 1.7 nautical miles from Iranian waters when they were captured.
Royal Marine Captain Chris Air, 25, from Altrincham, Cheshire, said the crew had made it clear they were on a "routine operation allowed under a UN mandate" but that the Iranians had a "planned intent."
Lt Carman said they were taken to a prison in Tehran where they were stripped and dressed in pyjamas.
They were kept in stone cells, sleeping on blankets and held in isolation until the last few nights and frequently interrogated.
The only woman in the group, Leading Seaman Faye Turney, believed for at least four days that she was the only one still being held.
In a statement, her parents - Alan and Rosalind Boswell - said they were "relieved" that Faye and her colleagues had returned home safely.
"They are now safely at home but in our minds it was never a foregone conclusion that they would return safely, and so soon," they said.
The BBC's Frances Harrison, in Tehran, said Iran insists the press conference revelations were the result of sailors "being briefed" by the UK government who "dictated to them".
The navy is reviewing the circumstances surrounding the incident and the wider rules of engagement for UK forces operating in the area.