They remain the subject of a sovereignty dispute between Britain and Argentina, with the two countries waging a brief but bitter war over the territory in 1982.
A British military task force ejected Argentine forces, who had landed on the Falklands to stake a territorial claim.
The 74-day conflict led to the deaths of 255 British military personnel, three islanders and 649 Argentine soldiers.
The prime minister’s official spokeswoman said: “Our position is unchanged, self-determination rests with the islanders and our commitment to the Falklands will never waver.”
She said any potential action against Argentina players who unveiled the banner was “a matter for Fifa”, but echoed the view of the Business Secretary Peter Kyle that world football’s governing body should investigate.
In 2013, the people of the Falkland Islands voted overwhelmingly in favour of remaining a UK overseas territory.
Of 1,517 votes cast in the two-day referendum – on a turnout of more than 90% – 1,513 were in favour, while just three votes were against.
Speaking in the House of Commons, Liberal Democrat MP Al Pinkerton condemned the “disgraceful scenes” in Atlanta and said “football was used as a platform to challenge the democratic right of Falkland Islanders to determine their own future”.
Replying for the government, Foreign Office Minister Stephen Doughty said it was a “real shame that people couldn’t focus on the football”.
He told MPs: “We have absolutely no doubt about our sovereignty over the Falkland Islands and the surrounding maritime areas.
“The Falkland Islands are British, they remain British and they will continue to be British and Falkland Islanders want to be British and they have explained that many, many times. Let’s get back to focusing on the football.”
