The German and Italian tourists and 16 members of a fishing boat's crew were intercepted after leaving the Maldives.
One minister said they were sailing to Diego Garcia, a British-controlled atoll that hosts a US military base.
One of the tourists said the claims they were going to Diego Garcia were "absolutely ridiculous".
Giorgio Rosi Belliere, an Italian businessman on board the boat, said they were on a whale watching tour and were not travelling to the atoll, some 750km (470 miles) away.
"We have done nothing wrong," he told the Maldives' Minivan News.
The Maldives Minister for Defence, Mohammed Zuhair, said the crew had failed to comply with international and local law on leaving the Maldives.
The Haveeru Online news site said the crew had not brought their passports, even though they were in international waters.
There are conflicting reports as to whether those on board were arrested. Minivan News said they had all now been barred from leaving the Maldives.
Diego Garcia is a highly-guarded military base once used for bombing raids on Iraq and Afghanistan.
In January, a former senior official in the George W Bush administration said the US government carried out interrogations of terror suspects at the base.

The Hammers said they chose the group for its "close links to the community".
Vice-chairman Karren Brady said the deal demonstrated the club had kept its promise to regenerate two areas of east London through its stadium move.
The developer plans to build new homes on the site as well as retail and leisure facilities by 2018.
It has also been in talks with the family of former West Ham and England captain Bobby Moore about the possibility of placing a landscaped garden named in his honour at the centre of the site, as well as a statue of him.
In a statement, Moore's daughter Roberta Moore said: "I have always believed that there should be some form of permanent West Ham United presence at the Boleyn Ground site after the team leave and I'm really pleased that the centre point of the development is planned to be named in honour of my father."

Eamon Bradley, from Benview Estate in Coshquin, was arrested in October 2014, after he returned from Syria.
He is charged with providing training in the making or use of firearms in Syria.
He is also charged with possessing a grenade in Syria with intent to endanger life.
The charges relate to dates between 4 January and 28 October 2014.
Mr Bradley was arrested at his then home in Melmore Gardens in the Creggan area of Derry.
A solicitor told Londonderry Magistrates Court that she was still awaiting the results of investigations being carried out by members of the Police Service of Northern Ireland's E-crime branch.
She said the investigating officer was now in receipt of a number of computer downloads that contain 9,000 images, all of which have to examined forensically.
A four-week adjournment in the case was granted and the defendant was released on continuing bail.
The Maldives military says it stopped seven tourists it claims were sailing to a highly-guarded US military base in the Indian Ocean.
[NEXT_CONCEPT]
West Ham have agreed to sell Upton Park to London developer the Galliard Group once they have completed their move to the Olympic Stadium in 2016.
[NEXT_CONCEPT]
Nine thousand images are to be inspected in the case of a Londonderry man charged with committing terrorist offences in the Middle East.