The dinghy, which contained military type rations of Argentinian origin, a torch, a camera and some clothing sparked a major security alert after it was found on a north beach on the easternmost island.
Councillor Norma Edwards, from the island's legislative council told BBC Radio 4's Today programme: "There are fringe groups in Argentina who would still I'm sure want to come and plant the Argentinian flag, if they could get the chance.
"We thought immediately it was a group of these people."
A treaty between Britain and Argentina, signed in July 1999, allows Argentinians to visit the Falkland Islands for the first time since the war in 1982.
However, the island's 2,200 inhabitants feel vulnerable to maverick Argentinian elements who might try to destabilise their community despite the treaty.
The British military garrison, Falkland Islands police and civilians scanned the sea and land for potential invaders, but so far nobody has been found.
A Royal Air Force C130 aircraft was also used to patrol the surrounding area of sea.
The Argentinian authorities have reported no vessels missing in the intervening period since the dingy was found on 28 December.
The dingy had the capacity for three people and rescue services now believe the abandoned supplies suggest the occupants were probably lost at sea.
"Our immediate reaction was that some Argentinians have come ashore but they have still not been found and there are no unaccounted human beings wandering around," Councillor Edwards said.
On 1 January the Argentinian Government again staked its claim for sovereignty to the island.
However, its President, Fernando de la Rue, has pledged himself to work for a negotiated settlement to the islands which have been in dispute since 1833.