The North Korean women's football team walked off the pitch at their Olympic match in Glasgow after their images were shown on a screen beside a South Korean flag.
Kick-off was scheduled for 19:45 BST but the game started over an hour late.
North Korea beat Colombia 2-0 in the second of the Olympic matches held at Hampden Park on Wednesday.
Games organisers in London have apologised to North Korean officials for the mistake.
The error occurred when a video package was being shown ahead of kick-off, with the North Koreans noticing that their faces were being pictured alongside the South Korean flag.
The squad walked off and could only be persuaded to return when the teams were announced again with each player's face displayed next to the North Korean flag.
The BBC's sports editor David Bond said it was an "embarrassing mistake" and not the start Games organisers would have wanted on the first day of sporting action, but "no great harm was done".
Relations between the two Koreas are tense - they remain technically at war following the 1950-53 Korean conflict, which ended in an armistice.
Speaking after the match, North Korea's coach Sin Ui Gun said: "Our team was not going to participate unless the problem was solved properly.
"Unfortunately it took some time later for the broadcast to be done again properly and we made the decision to go on with the match."
He added: "Our players cannot be shown especially with other flags, especially the South Korean one.
"If this matter had not been solved, continuing would have been a nonsense."
A statement released by London 2012 organisers said: "Today ahead of the women's football match at Hampden Park, the South Korean flag was shown on a big screen video package instead of the North Korean flag.
"Clearly that is a mistake, we will apologise to the team and the National Olympic Committee and steps will be taken to ensure this does not happen again."
It was not immediately clear who had produced the video shown in the stadium.
London 2012 spokesman Andy Mitchell said: "The South Korean flag was shown in the video package on the screen before the kickoff and the North Koreans were naturally very upset about that.
"We have made a full apology to the team and the North Korean NOC. A genuine mistake was made for which we apologise."
South Korea will face North Korea in the first round of the men's Olympic table tennis team event after the pair were drawn against each other on Wednesday.
The first event of the Olympics got under way at 1600 BST at Cardiff's Millennium Stadium on Wednesday and ended in a win for Team GB over New Zealand in the women's football. Two matches also took place at the City of Coventry stadium.
In other Olympics news:
- Prince Charles and the Duchess of Cornwall visited Tottenham, north London, to greet the Olympic flame . Olympian Daley Thompson was the final torchbearer of the day
- The launch of Games Lanes in London has caused confusion , with some of the lanes still open to everyone, and signs on some stretches apparently offering conflicting advice to motorists
- The final dress rehearsal for the opening ceremony took place at the Olympic Stadium, in Stratford, east London
Meanwhile, thousands of Games spectators have arrived in London, on one of the busiest days for Heathrow airport.
A strike by border staff, due to take place on the eve of Friday's opening ceremony, has been called off by union officials.