MELBOURNE (Reuters) - Authorities in Fiji on Saturday detained the leaders of two opposition parties and a senior trade union official after they took part in an event critical of the Pacific island nation's constitution, an opposition party official said.

The leader of the National Federation Party (NFP), Biman Prasad, and a trade unionist, Attar Singh, were taken into custody over their participation in Wednesday's forum on the 2013 constitution, said an NFP official, Prem Singh.

"The arrest is a threat to public assembly and we don't know why they are being arrested, they are only doing their jobs," Singh said, but added that no charges had yet been made.

In a statement, the Sodelpa opposition party said its leader Sitiveni Rabuka, a former prime minister, had turned himself in to police. Rabuka was involved in two previous coups in 1987 and went on to become prime minister between 1992 and 1999.

Police and government officials did not immediately respond to telephone calls from Reuters seeking comment.

But a Fiji police spokeswoman, Ana Naisoro, told The Fiji Times that several people were being questioned over comments made at the forum which "could affect the safety and security of all Fijians".

"This step is being taken merely to eliminate all doubts and concerns that could stem from speculation," Naisoro was quoted as saying by The Fiji Times.

Police are also holding a former politician and an official of a non-government body that organized Wednesday's event, Radio New Zealand said. The event coincided with the tiny nation's first public holiday for Constitution Day.

Speaking to the Australian Broadcasting Corporation the day before the event, Prasad had described the holiday as a "waste of money" and government "propaganda".

"There is nothing much to celebrate about the 2013 constitution, which was opposed to the will of the people," Prasad said.

Prasad's wife, Rajni Chand Prasad, told Reuters that police had searched their house looking for documents and that police also searched his office and took away a laptop computer.

Fiji's Prime Minister Frank Bainimarama came to power in a bloodless military coup in 2006. He stood down from the military to run as a civilian in the country's 2014 elections, winning by a landslide.

(Reporting by Jarni Blakkarly; Editing by Clarence Fernandez and Himani Sarkar)