Inspector Markos Christou revealed the alleged confession to a Larnaca court. The men appeared in court in handcuffs and dressed in khaki overalls. Each replied 'no' when asked if they had anything to say before Judge Andonis Indianos ordered that they be detained for eight days while police inquiries continued.
Louise Jensen, 23, was grabbed early yesterday while riding a motorcycle with a friend near the south coast resort of Ayia Napa, according to police.
The soldiers were arrested at a roadblock about an hour later when the friend, Michalis Vassiliades, identified them.
They were named in court as Alan Ford, 26, Justin Fowler, 26, and Jeff Parnell, 23, all of the First Battalion of the Royal Green Jackets based in Dhekelia, 15 miles from Ayia Napa. Their hometowns and ranks were not disclosed.
Insp Christou said Mr Fowler told police during questioning that the soldiers killed Miss Jensen and buried her body in a field near Ayia Napa.
He was said to have taken police to where he said Miss Jensen, the Cyprus representative of a Danish tour agency, had been buried, 'but we were unable to locate the spot', Insp Christou told the court.
He quoted Mr Vassiliades, a 21- year-old waiter, as saying the couple had stopped their motorbike at a petrol station near Ayia Napa where a yellow Mini Moke beach buggy was also stopped. The buggy pulled away slowly and the couple tried to overtake, but the car pushed them to the side of the road and they fell off. The car then reversed and hit them, he allegedly told police.
Two of the soldiers got out of the car and one picked up a spade and hit Miss Jensen. Mr Vassiliades said he ran off through trees, but saw the men throw Miss Jensen violently into their car and drive off. Mr Vassiliades then ran to a police station for help.
Police set up roadblocks in and around Ayia Napa. Shortly afterwards the soldiers were arrested and blood stains were found in the buggy and on their clothes and two shovels were found in the vehicle, Insp Christou said.
A British army spokesman confirmed that three soldiers serving at the British Sovereign Base in Dhekelia had been arrested in connection with a 'serious incident'.
Major Robert Shaw said: 'We are offering the Cyprus police every possible assistance. We have already supplied three Sovereign Base Area police search teams.'
Britain maintains two sovereign bases in Cyprus manned by some 4,000 troops.