The International Olympic Committee (IOC) has asked South Korea to bar footballer Park Jong-woo from the bronze medal ceremony after he held up a political message after the team beat Japan.
The slogan was said to refer to a long-running dispute about islands which both South Korea and Japan claim.
The IOC says it is holding an inquiry.
Friday’s match came hours after South Korea’s president visited the islands, known as Dokdo in South Korea and as Takeshima in Japan, sparking a row.
The move prompted Japan to recall its ambassador in Seoul.
IOC has asked South Korea to bar Park Jong-woo from the bronze medal ceremony after he held up a political message after the team beat Japan
South Korea won the Olympic football bronze medal by beating Japan 2-0.
The IOC says that after the game, a player was photographed brandishing a sign allegedly asserting South Korea’s sovereignty over the islands.
The committee urged the South Korean Olympic committee to take “swift action on this issue” and said the player should not be present at the medal ceremony, which took place on Saturday.
A Korean Football Association official later named him as Park Jong-woo, 23 – who was not present at the ceremony.
Football’s governing body, FIFA, said it had opened a separate investigation to discipline him.
The official told South Korea’s Yonhap news agency that Park Jong-woo had taken the sign – which reportedly read “Dokdo is our land” – from a fan after the match, stressing that the incident was not pre-planned.
“Park was running around with the banner which he got from the crowd. We saw the message on the banner so we quickly took it from him,” the unnamed official is quoted as saying.
The statutes of both the IOC and FIFA prohibit political statements by athletes and players.
Friday’s visit by South Korean President Lee Myung-bak to the islands was strongly criticized by Japanese Prime Minister Yoshihiko Noda.
“It is contrary to our nation’s stance that Takeshima is historically – and under international law – an integral part of our national territory, and is completely unacceptable,” PM Yoshihiko Noda said.
The uninhabited islands, which are roughly equidistant from the two countries, are small but lie in fishing grounds which could also contain large gas deposits.
Mexico has beaten Brazil with 2-1 at Wembley and has won the men’s Olympic football gold medal for the first time.
Oribe Peralta struck from the 18-yard box after 32 seconds following some poor Brazilian defending.
Fabian Marco hit the Brazil crossbar before a completely unmarked Oribe Peralta headed his team’s second goal.
Brazil, also hoping to win gold for the first time, pulled a goal back through Hulk in injury-time, before Oscar headed wide when well positioned.
But the South American side scarcely deserved to take the game into extra-time after a very patchy performance, particularly in defence.
Mano Menezes’s team had scored three in each of their previous five games and were treating the tournament as an important staging post ahead of hosting the World Cup in 2014.
But if they are to succeed on home soil they will have to show a significant improvement from what they produced at Wembley, with star forward Neymar a largely peripheral figure.
Mexico has beaten Brazil with 2-1 at Wembley and has won the men's Olympic football gold medal for the first time
Mano Menezes went into Saturday’s match under huge pressure to deliver gold and fill the one significant missing blank for the Brazilian team, but if the game was to be Brazil’s coronation as Olympic champions then Mexico clearly had not read the script.
They defeated Brazil 2-0 in a friendly earlier in the summer and stunned Wembley when Peralta’s low strike nestled in the bottom corner while many inside the stadium were still taking their seats.
Manchester United defender Rafael was partly at fault for the goal, his sloppy pass allowing Javier Aquino to nip in and dispossess Sandro, with the ball running invitingly into the path of Oribe Peralta.
Brazil could not find their stride – a situation not helped by a series of niggly fouls that broke up play and angered coach Mano Menezes, who could be seen waving an imaginary card on the touchline.
And their disappointing start was put into stark perspective when Mano Menezes made a change just after the half-hour mark, bringing on Hulk for Alex Sandro.
The substitution made a difference and Jose Corona managed to palm clear a swerving strike from Hulk while Marcelo shot wastefully wide after he had linked with Oscar and Leandro Damiao to carve open the left side of the Mexican defence.
By the early stages of the second half it was obvious that Mexico had opted to try to defend their lead.
This seemed to play into the hands of their opponents, particularly Neymar, who had disappointed in the opening half but briefly relished the chance to repeatedly run at the Mexico defence.
He twice shot wide and saw another effort blocked, but his influence soon faded and Mexico almost struck with a swift break.
There was more shoddy Brazilian defending involved too, as Fabian dispossessed an opponent far too easily and eventually saw his overhead effort rebound off the crossbar.
An unmarked Oribe Peralta later slotted home from six yards but Brazil were saved by the offside flag. There was to be no reprieve with 15 minutes remaining.
A free-kick was delivered from the right and the Mexico striker was left completely alone to head home from eight yards.
Brazil’s frustrating afternoon saw team-mates Juan Jesus and Rafael square up to each other in the final minutes.
Hulk’s injury-time strike into the bottom corner briefly ignited hope of a spectacular comeback and Oscar then headed wastefully wide at the near post as Mexico held on.
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