LONDON — Hopes were rising yesterday for an early release of the 15 sailors and royal marines held in Iran after one of the country’s most senior politicians said they would not face a show trial.

During an interview on Channel 4 News, Ali Larijani said the situation was “quite resolvable.”

There were grounds for further optimism when the chief of the Iranian National Security Council said the 11-day crisis could be resolved by diplomatic means.

“I definitely believe that this issue can be resolved, and there is no need for any trial,” Mr. Larijani said in the interview with Jon Snow.

“Our priority is to solve the problem through proper diplomatic channels. We are not interested in having this issue get further complicated.”

A path for a resolution to the impasse appeared to be mapped out by Mr. Larijani after he ruled out a trial.

He suggested Britain would need to send a diplomatic delegation to Tehran, confirm that its navy had made a mistake by straying into Iranian waters, and guarantee that the error would not be repeated.

The politician gave further hope to the anxious families of the eight sailors and seven marines, saying it was “our interest to solve the problem as soon as possible.”

There was “no benefit” in keeping British troops “away from their families from a humanitarian view,” he said.

However, he insisted that the navy had strayed into Iran and had GPS evidence to prove it.

The government says it has documentary proof that the boarding party of two fast boats was two miles inside Iraqi territorial waters when they were arrested on March 23.

After telling parliament that the boats had not violated Iran’s sovereign territory, it would be a humiliating climb-down for Prime Minister Blair if he were forced to confess the error.

Mr. Larijani said Britain should be “brave enough” to admit “their mistake, confess to it and leave.”

“The solution is very clear,” he said. “First of all, they have to put aside the irrational moves and resorting to the language of force. Secondly, there is a difference of view between the U.K. government and the Iranian government and this issue should be resolved bilaterally. They should clarify the fact of whether they have been in our territorial waters or not.”

He appeared irritated by the government accusing Iran of taking the service personnel hostage and said the European Union had “started to condemn Iran without knowing the facts.”

He accused the E.U. of using “the language of force” by expressing “unconditional support” for Britain and threatening “appropriate measures” unless the captives were released quickly.

Before Mr. Larijani’s interview the prime minister’s spokesman said there was “a lot going on behind the scenes.”

It appeared that the Iranian politician’s appearance on live British television was Iran’s response after an exchange of notes with the British embassy in Tehran.

“The Iranians know our position. They know that stage-managed TV appearances aren’t going to affect our position,” a Foreign Office spokesman said.

Mr. Larijani appeared to indicate that there would be no further televised appearances by British personnel confessing and apologizing for entering Iran.

It had been claimed that all 15 British service personnel had confessed to illegally entering the country’s waters, but state-run radio in Iran reported that any further confessions were not being broadcast because of “positive changes” in Britain’s stance.

A Foreign Office spokesman said last night: “We are still studying Dr. Larijani’s remarks.