Cristina Kirchner, the Argentine president, signed the decree on Tuesday, with a drilling rig from Scotland due to arrive in the islands and start drilling next week.
Britain's foreign ministry rejected Argentina's demand, maintaining Buenos Aires cannot control the territorial waters surrounding the Falklands.
"Regulations governing Argentine territorial waters are a matter for the Argentine authorities," the ministry said.
"Any attempt by Argentina to claim any sort of rights of sovereignty over that region is something we should take very seriously"
Andrew Rosindell MP
"This does not affect Falkland Islands territorial waters which are controlled by the island authorities."
However, Rosindell, a member of the opposition Conservative Party, whose leader and then premier, Margaret Thatcher, sent troops in to seize back the Falklands after the Argentinians invaded, called on the foreign ministry to take further action.
"It is 28 years since the Falklands War and it has been made clear to Argentina that they have no say over the Falkland Islands or their territorial waters and they should not try to interfere with them," he said.
"Any attempt by Argentina to claim any sort of rights of sovereignty over that region is something we should take very seriously.
"I don't think we should appease Buenos Aires, we found out what happens last time."
Several British oil companies plan to start exploration of the area with an offshore rig, and numerous areas have been licensed for development of oil and natural gas reserves.
Victorio Taccetti, Argentina's deputy foreign minister, said his country would take "adequate measures" to stop any oil and gas exploration off the islands.
He told Argentina's Millennium radio station that the British government "shouldn't be complacent, because they see that Argentina defends its rights - obviously by peaceful means, such as through bilateral and multilateral action in [international] bodies".
Britain and Argentina have disputed sovereignty over the islands since the early 19th century, and negotiations over their status dragged on until early 1982, when Argentina's military rulers opted to take the territory back by force.
The Argentines invaded on April 2, sparking a brief war in which some 650 Argentine troops, more than 250 British personnel and three islanders were killed.
Britain and Argentina re-established full diplomatic ties in 1990. Buenos Aires continues to claim the islands as its own, but has made a commitment not to use force to press its claim.