The newspaper said Movahedian spoke before Friday's news conference at which several of the freed personnel alleged that they had been blindfolded, bound, kept in solitary confinement and subjected to psychological pressure during their captivity.
"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," Movahedian was quoted as saying.
He said "the prime issue for Iran" was recognition of its right to a nuclear power programme.
The US and allies, including Britain, fear Iran is pursuing a nuclear weapons programme but Tehran insists the programme is purely civilian.
The British marines said after their return that they were coerced into saying they had been in Iranian waters when they were detained.
"All of us were kept in isolation. We were interrogated most nights and presented with two options: If we admitted that we'd strayed, we'd be on a plane to [Britain] pretty soon," Lieutenant Felix Carman, who commanded the crew, said.
|Britain criticised Iran for putting the detained |
naval personnel on television [EPA]
"If we didn't, we faced up to seven years in prison."
These claims painted a very different picture of their 13 days in detention than comments they made on Iranian television.
"Since we've been captured we've been treated with a great deal of respect and dignity.
"All our needs have been looked after and catered for," Carman said while being held by Iran.
A British foreign office spokesman said Britain "will need to time to assess the implication for diplomatic relations with Iran" of the crew's accounts of their treatment.
Tehran has dismissed the allegations made at the news conference as British government propoganda, just as London condemned Iran for frequently displaying the captured naval personnel on state television.
On Saturday, an adviser to Mahmoud Ahmadinejad, Iran's president, denied that the personnel had been mistreated, saying they had made such claims under pressure from their superiors.
Ali Akbar Javanfekr said: "The mistreatment of the sailors is a lie. The British authorities should know that they cannot keep hiding the truth from the British people.
"We envisioned that the 15 sailors would be subjected to pressure by British security and intelligence forces."
For that reason, Javanfekr said, "President Ahmadinejad asked Prime Minister Tony Blair not to put pressure on the sailors for having told the truth, but (he) did not hear this humanitarian appeal.
"London's attitude was foreseeable, because expression of the truth by the sailors would have been a challenge to the British government and army."
He said Tehran could have organised its own "meeting of the sailors with journalists in Iran so that they could ask whatever they wanted but it did not do so to avoid the sailors having problems" when they got home.