Geologists say the seabed around the Falklands has substantial oil reserves
The UK has made "all the preparations that are necessary" to protect the Falkland Islands, Prime Minister Gordon Brown has said.
However, the Ministry of Defence has denied reports that a naval taskforce is on its way to the Falklands.
Argentina has brought in controls on ships passing through its waters to the islands over UK plans to drill for oil.
Shadow foreign secretary William Hague told the BBC the Royal Navy's presence in the region should be increased.
The Sun newspaper reported that up to three ships were to join the islands' regular patrol vessel.
BBC defence correspondent Caroline Wyatt understands the destroyer HMS York and the oil supply tanker RFA Wave Ruler are in the area, as well as HMS Clyde, which is permanently based there.
However, the MoD said Britain already had a permanent naval presence in the South Atlantic as well as more than 1,000 military personnel on the islands.
Speaking on Gateshead-based Real Radio in the North East, Mr Brown said he did not expect to send a taskforce to the area.
Caroline Wyatt, BBC defence correspondent
It's clear that Britain has the military assets it needs in or around the Falkland Islands to back up its diplomacy with Argentina - on the principle that diplomacy succeeds best when a nation can talk softly but carry a big stick.
The MoD will only say that it is "maintaining" a deterrent force in the area, and that this is not a new taskforce - but it leaves little doubt that the UK has the means to defend the Falkland islanders already in place to back up its diplomatic stance.
But at the same time, the British government does not want to escalate the current row with Argentina, even as it remains firm on Britain's right to explore for oil around the Falklands, with the prime minister and others emphasising that they see "sensible discussions" prevailing.
Earlier this week, Air Chief Marshal Sir Stephen Dalton, the head of the Royal Air Force, drew attention to the situation in the South Atlantic in a speech to the International Institute of Strategic Studies, referring to the "increasingly tense situation" around the Falkland Islands to stress the need for maintaining air superiority.
He said he hoped "sensible discussions" with Argentina would prevail, adding: "We have made all the preparations that are necessary to make sure the Falkland islanders are properly protected."
Foreign Secretary David Miliband said all UK oil exploration in the area was "completely in accordance with international law".
He added: "We maintain the security of the Falklands, and there are routine patrols continuing."
After Argentina's invasion of the Falklands in 1982, a UK taskforce seized back control in a short war that claimed the lives of 649 Argentine and 255 British service personnel.
The BBC's Andrew Harding in Buenos Aires said it was difficult to find anyone in Argentina who believed the Falklands were in danger of being at the centre of a military conflict.
But Argentine Deputy Foreign Minister Victorio Taccetti said his country would take "adequate measures" to stop oil exploration.
Meanwhile, speaking on BBC Radio 4's Today programme, Mr Hague called for "some sort of increased naval presence - it may just be one more ship visiting more regularly" in the region.
He added: "That kind of thing would show very clearly to Argentina - with whom, again, we want friendly relations - that we will be very firm about this. It would send a signal not to misunderstand British intentions.
"One of the things that went wrong in the 1980s is that the Argentines thought we weren't really committed to the Falkland Islands. So, we mustn't make that mistake again. Our commitment should be very clear."
Buenos Aires claims sovereignty over the Falkland Islands, which it calls Islas Malvinas.
It has previously threatened that any company exploring for oil and gas in the waters around the territory will not be allowed to operate in Argentina.
On Tuesday, Argentine President Cristina Fernandez signed a decree requiring all vessels travelling between Argentina and the islands, or those wanting to cross Argentine territorial waters en route to the Falklands, to seek prior permission.
But a drilling rig from the Scottish Highlands, the Ocean Guardian, is nearing the islands and is due to start drilling next week, the UK-based company Desire Petroleum has said.
Last week, a ship carrying drilling equipment was detained by Argentine officials.
Geologists say the ocean bed surrounding the Falklands could contain rich energy reserves.
Last year, Argentina submitted a claim to the United Nations for a vast expanse of ocean, based on research into the extent of the continental shelf, stretching to the Antarctic and including the island chains governed by Britain.
It is due to raise the issue at the UN next week.
On Thursday, an MoD spokesman said the government was "fully committed" to the Falklands, adding: "A deterrence force is maintained on the islands."
Foreign Office Minister Chris Bryant said it was important not to lose sight of the fact that the UK and Argentina were "important partners".
But he added: "'We have no doubt about our sovereignty over the Falkland Islands and we're clear that the Falkland Islands government is entitled to develop a hydrocarbons industry within its waters."
The waters surrounding the disputed islands are considered by the UK to be part of the British Overseas Territories.
But Buenos Aires believes the UK is illegally occupying the Falklands, South Georgia and the South Sandwich Islands.