Michael Fallon paid tribute to the British casualties of the Falklands War as he became the first Defence Secretary to visit the islands in over a decade.
Around 1,400 British service personnel are still stationed on the South Atlantic islands that have remained until recently at the centre of a bitter war of words with Argentina.
However former president Cristina Kirchner left office two months ago, and her succession by Mauricio Macri has raised hopes of a thaw in relations with Buenos Aires.
"I hope that opportunity can now be taken," Mr Fallon said.
Ms Kirchner repeatedly raised the dispute with escalating rhetoric, asserting that the remote archipelago, known to Argentinians as the Islas Malvinas, should be returned.
Argentina has maintained Britain has occupied the islands illegally since 1833.
After an Argentine invasion in April 1982 a British naval task force was dispatched by Margaret Thatcher to retake the islands.
A total of 255 British lives were lost, with many hundreds more wounded.
In Port Stanley on Tuesday Mr Fallon bowed before a memorial obelisk in remembrance of the British servicemen killed in the conflict.
A handwritten note left on a wreath by the Defence Secretary read: "In grateful memory of those who sacrificed their lives for the liberation of these islands."
In a 2013 referendum Falklanders voted overwhelmingly to remain a British overseas territory.
Speaking to the Daily Telegraph, Mr Fallon criticised recent comments by Labour leader Jeremy Corbyn that Britain and Argentina should negotiate over the islands' sovereignty.
He told the newspaper: "The biggest threat at the moment isn't Argentina, it's Jeremy Corbyn and the Labour Party who want to override the wishes of the islanders."
He added: "The issue is how we improve relationships with rest of South America and we have the election of a new government in Argentina that may open the door to that."