The 15 Royal Navy personnel who were seized on Friday are being held at an Iranian Revolutionary Guards Corps base in Tehran, the BBC has been told.
The 15 are based on HMS Cornwall, which patrols Iraqi territorial waters
An Iranian source told the BBC's security correspondent the Britons were being interrogated to find out if their mission was intelligence-gathering.
The investigation involved examining tracking equipment to determine exactly where the crew was captured.
It would probably take a minimum of days, the highly placed source said.
The BBC's security correspondent Frank Gardner was told the interrogation was being carried out by officials from Security, Intelligence and the Judiciary.
In order for the Britons to be released "every vested interest in Iran would need to be satisfied they had not deliberately entered Iranian waters, nor were they spying", the source said.
Those interests included those of the Revolutionary Guards, the foreign ministry, the judges and the intelligence ministry.
'Fit and well'
The seized personnel are fit and well, Iran has told the Foreign Office.
A senior Iranian official had previously told the UK's ambassador in Tehran that the Britons were being held in Iran but would not disclose their exact location.
He said Iran was "working to resolve the matter as soon as possible".
Iran says the Britons could be charged with illegally entering Iranian waters, although both Iraq and the UK insist they were in an Iraqi area.
British ambassador Geoffrey Adams was assured that the eight sailors and seven marines were well during an hour-long meeting on Monday with Ebrahim Rahimpour, a senior official at the Iranian foreign ministry in Tehran.
Mr Rahimpour agreed to stay in close touch with the British embassy but declined to say what plans Iran had for their release, according to a statement from the Foreign Office.
The Iranian state news agency IRNA said Mr Rahimpour told Mr Adams that the 14 men and one woman could face legal proceedings.
It claimed he expressed concern about the escalation of tensions following the US occupation of Iraq which created security problems on Iran's borders.
And after "contradictory statements" over the seizure of the Britons, the case "required an inquiry into such suspicious events".
Mr Adams's meeting with Iranian officials was the second in two days in which he tried to get consular access to the navy personnel.
It came as Tony Blair said Britain was "utterly confident" the naval personnel were in Iraqi waters and repeated his call for their release.
Defence Secretary Des Browne later told the Commons the government was doing "everything possible" to secure the release of the detainees.
He said his thoughts were with the crew members of HMS Cornwall who had been detained, their friends in theatre and the families in the UK.
Liam Fox, the shadow defence secretary, said the Conservatives wanted MPs to have a chance to discuss the issue as soon as diplomatic sensitivities allowed.
In a telephone call on Sunday night, Iraqi foreign minister Hoshiyar Zebari told his Iranian counterpart Manouchehr Motakki the Britons had been in Iraqi waters when captured.
Mr Zebari said they were working with the multi-national forces with the approval of the Iraqi government and according to UN Security Council resolutions.
Iraq's foreign ministry added: "The minister called for the release of the detainees and to deal with this case in a wise way."
The Britons, who include one woman, were seized at gunpoint after inspecting an Iraqi boat and returning to their two small boats to head back to HMS Cornwall.
Students belonging to the paramilitary Basij group, which is close to Iranian President Mahmoud Ahmadinejad, have called for them to be put on trial.
Dr Ali Pahlavan, the executive editor of Iran News - an independent newspaper in Tehran - told BBC Radio 4's Today programme the "ultra conservative" Revolutionary Guard believed that Britain and the US needed to be challenged.
"This could be part of the strategy to challenge British and American supremacy in this part of the world - which is troubling, because this could lead to confrontation and this could be a trigger and could lead to escalation".