Former Conservative leader Lord Howard has said Theresa May would show the same resolve to defend Gibraltar as Margaret Thatcher did over the Falklands.
The peer told Sky News' Sophy Ridge on Sunday show: "I think there's no question whatever that our Government will stand by Gibraltar.
"Thirty-five-years-ago this week, another woman prime minister sent a task force half way across the world to defend the freedom of another small group of British people against another Spanish-speaking country.
"I'm absolutely certain that our current Prime Minister will show the same resolve in standing by the people of Gibraltar."
Shortly afterwards, Mrs May pledged to work with Gibraltar to get "the best possible outcome on Brexit" for the British territory.
The Prime Minister said the UK remained "steadfastly committed" to the Rock amid concerns it could become a "bargaining chip" in Brexit negotiations.
Spain has a long-standing territorial claim on Gibraltar, which has been held by the UK since 1713 and has the status of a British overseas territory.
Draft Brexit negotiating guidelines, sent out on Friday, contained a clause suggesting Spain will be able to veto any future trade deal between the EU and the UK.
Mrs May, who has been criticised for not mentioning the territory in her Brexit letter to the EU, spoke to Gibraltar's chief minister Fabian Picardo to reassure him and the people of Gibraltar over their status.
A Downing Street spokeswoman said Mrs May "reiterated our long-standing position that the UK remains steadfastly committed to our support for Gibraltar, its people and its economy".
"The Prime Minister said we will never enter into arrangements under which the people of Gibraltar would pass under the sovereignty of another state against their freely and democratically expressed wishes, nor will we ever enter into a process of sovereignty negotiations with which Gibraltar is not content.
"The Prime Minister said we remain absolutely dedicated to working with Gibraltar for the best possible outcome on Brexit and will continue to involve them fully in the process."
Mr Picardo, who has hit out at the threat of a Spanish veto on the Rock's future, said he was "sure the UK will be batting for Gibraltar".
He told the Andrew Marr Show: "The United Kingdom goes to war over the principle of consent around the world, and the people of Gibraltar have expressed their views as to what they think the sovereignty of Gibraltar should be democratically and freely."
Liberal Democrat leader Tim Farron said it was "unbelievable" that within a week of triggering Article 50 "there are Conservatives already discussing potential wars with our European neighbours".
He said: "Brexiteers have gone from cheering to sabre-rattling ... it is absolutely ludicrous."
Sky's Political Correspondent Lewis Goodall said: "In her latter years as Prime Minister, Margaret Thatcher used to tell a story.
"For visitors lucky enough to receive a personal tour from the PM around Chequers, she pointed out a certain desk and uttered what must have seemed rather ominous words: 'That is the chair I sat in when I gave the order to sink the Belgrano'.
"Perhaps that's the sort of "resolve" Michael Howard had in mind when he spoke this morning.
"Either way it's hardly going to do much to ameliorate Anglo-Spanish relations, which have had a rough week.
"When speaking of 'another Spanish-speaking nation', I doubt very much the Spanish government would much appreciate the comparison with Argentina in 1982, run by a military junta.
"Whatever the Spanish PM Mariano Rajoy might be, General Galtieri he ain't.
"The comments aren't likely to make the Gibraltar tussle any better. Nor are the Spanish Foreign Minister's in El Pais today where he confirmed that Spain would not veto an independent Scotland's entry into the EU.
"The negotiations haven't even begun yet. And they've already been waylaid by a tiny rock on the Mediterranean. Not the best start."