The incident happened after Argentina beat England 2-1 in a World Cup semi-final on Wednesday in Atlanta.
During post-match celebrations, Argentine players held a banner handed over by fans in the stands, reading "Las Malvinas son Argentinas" — "The Malvinas are Argentine."
Argentina refers to the Falkland Islands as Islas Malvinas. They were invaded in 1982 under orders from Argentina's then-military dictatorship, triggering a 10-week war won by Britain.
"The World Cup might not be ours, but the Falkland Islands definitely are," a spokesperson for Prime Minister Keir Starmer said on Thursday.
"Self-determination rests with the islanders and our commitment to the Falklands will never waver."
Starmer supported calls for FIFA to investigate, the spokesperson added, after UK Business Secretary Peter Kyle said the players' behaviour was "entirely inappropriate".
FIFA can prosecute Argentina's players and soccer federation because their disciplinary code prohibits at stadiums any "message that is not appropriate for a sports event" including those of "a political, ideological, religious or offensive nature".
FIFA fines for political messaging can range between $7,100-$29,000 (US$5,000-$20,000).
Soccer's world governing body have not yet commented on the incident.
A FIFA disciplinary case under previous leadership banned a South Korea player for two 2014 World Cup qualifying games because he held up a similar banner about a territorial claim against Japan at the 2012 London Olympics.
Park Jong-woo took a fan banner with the slogan "Dokdo is our territory" after South Korea beat Japan in the men's bronze-medal game.
On Wednesday, Argentina player Lisandro Martínez was asked if the banner could have stirred deep emotions and tears for a veteran of the Malvinas conflict.
"We couldn't let the Argentine people down" said Martínez, who has played in England for the past four years with Manchester United.
"It is a sad part of our history," Argentina player Leandro Paredes said in Atlanta about the banner, "for everyone involved in that chapter of, I repeat, our history. And it hurts. We knew we were playing for them, too."
Kyle, an influential British minister, said: "The World Cup has one of its central tenets that politics is separate from football. That is now a matter for FIFA."
Argentinian Vice President Victoria Villarruel wrote on X before the game: "We play against the usurping pirates.
"I'm not going to be politically correct or cold-hearted; against the English, it's always something more."
And she tweeted a victory message at fulltime saying, "it wasn't just another match" alongside a video of what appeared to be Argentinian soldiers.
Villarruel's father fought in the Falklands War for Argentina's military dictatorship.
With DPA.
6°C