The five Britons are being detained by the Iranian navy after the Volvo 60 yacht was stopped on 25 November.
The Foreign Office said Luke Porter, Oliver Smith, David Bloomer, Oliver Young and Sam Usher may have "strayed inadvertently into Iranian waters".
The Team Pindar-backed yacht was sailing from Bahrain to Dubai.
Esfandiar Rahim-Mashaie, President Ahmadinejad's head of staff, told Iran's Fars news agency: "Judiciary will decide about the five... naturally our measures will be hard and serious if we find out they had evil intentions."
Foreign Secretary David Miliband said he was expecting the Iranians to make a statement later on Tuesday.
He also said he hoped the matter would be resolved "soon" and that there was "no confrontation or argument".
Mr Miliband said: "This is a human story of five young yachtsmen. It's got nothing to do with politics, it's got nothing to do with nuclear enrichment programmes... it has no relationship to any of the other, bigger issues."
He added: "They were going about their sport and it seems they may have strayed inadvertently into Iranian waters."
The Foreign Office says it believes the five sailors are being held on the island of Sirri. It said it was seeking confirmation of this from the Iranian authorities. The sailors are understood to be safe and well.
Dubai-Muscat Offshore Race organisers said the crew of the Kingdom of Bahrain yacht, who were preparing for a race, may have been "drifting" after experiencing propeller problems.
Louay Habib, from the Dubai Offshore Sailing Club, told the BBC the shore crew for the boat had said "there was no wind at the time, and they told us that they were organising for a tow to come and get them".
He added: "It's purely speculation but they would have probably been drifting... in 10 hours they could well have strayed into Iranian waters."
David Young, said his 21-year-old son, Oliver, was a "fanatical yachtsman" with a great deal of experience and that he was certain his son would be able to "cope with this very well".
But Charles Porter, of Weston-super-Mare, who is the father of 21-year-old Luke, said he and his wife Beverley were concerned.
He said: "We are holding things together as a family at the moment. I haven't spoken to him since yesterday. He was as good as can be expected."
The fiancee of Sam Usher, 26, Nicola Drayton, said: "It's difficult but you just get on, you have no choice."
Of the remaining two captives, Mr Smith, 31, is an engineer from Southampton and his teammate Mr Bloomer is said to work as a sports broadcaster in Bahrain.
The FCO said the men had been on their way to take part in the Dubai-Muscat race.
The British Embassy in Tehran is demanding the immediate release of the five but has so far only had indirect contact with the crew members.
Full story: www.bbc.co.uk