Ali Larijani, head of Iran's supreme national security council, said late on Monday that dialogue would provide a solution to the standoff.
"We definitely believe that this issue can be resolved and there is no need for any trial," he told Britain's Channel Four television.
Larijani criticised the EU's position of "unconditional support" for Britain, saying that it had "started to condemn Iran without knowing the facts."
Britain maintains the sailors did not leave Iraqi waters during an operation in the Shatt al-Arab waterway.
"It is Iran's responsibility to find a quick solution"
Emkay, Auckland, New Zealand
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"All evidence, including the GPS carried by the British military and also the frank confessions of all 15 British personnel shows that they have entered Iran's territorial waters without permission," Iranian state television said earlier on Monday.
The ISNA news agency said that all 15 sailors had given confessions to camera of their entry into Iranian waters.
"But due to some changes in the past two days regarding the controversial British policies, television will not air the details of these interviews," it said.
On Sunday, Iran's Al Alam television also broadcast images with sound of two of the detainees.
Captain Chris Air, one of the 15 naval service personnel, was shown saying: "At about 10 o'clock in the morning, we were seized, apparently at this point here, from their maps, from the GPS they've shown us, which is inside Iranian territorial waters.
"So far we have been treated very well by the people here. They have looked after us and given us enough food," said Air, dressed in military uniform.
Britain insists the sailors and marines were on a routine anti-smuggling patrol in Iraqi waters, operating under a UN mandate.
"The Iranians know our position. They know that stage-managed TV appearances aren't going to affect that position. They know that we have strong international support," said an official spokesman for Tony Blair, Britain’s prime minister.
Blair's spokesman said that "a lot is going on behind the scenes" to secure their release. Britain has maintained bilateral relations with Iran and has an embassy in Tehran, unlike the US.
On Sunday, the British embassy was evacuated as 200 Iranian students demonstrated outside the compound.
They demanded that the 15 sailors and marines be punished, exploding firecrackers and chanting "death to Britain".
George Bush, the US president, has called the sailors and marines "hostages" and urged their release.
The standoff over the captured British sailors comes amid continuing differences between Iran and western nations over Tehran's nuclear programme.
Washington says Iran's uranium enrichment programme is aimed at making atomic weapons, while Iran insists that the programme is for civilian power generation.