Players, officials and coaching staff touched down in the southern city of Rostov-on-Don on Monday following the malfunction, with footage of the drama posted on social media.
"According to the Saudi Arabian Football Federation, all the Saudi national team players have arrived safely in Rostov-on-Don this afternoon to play against Uruguay, and now are staying in their residence, and that the fire was merely an accident", one of the statements said.
The plane used by the Saudi Arabian football team caught fire on the way to their next World Cup destination.
The team did not clarify at what point during the flight the fire broke out.
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The videos uploaded to twitter show fire shooting from the engines underneath the wings. "Well, of course we were scared a bit, but thank God".
The side were travelling to Rostov where they play Uruguay on Wednesday.
The Saudis were beaten 5-0 by Russian Federation in the World Cup opener in Moscow last week.
It was while traveling for that match that the incident occurred but the football federation confirmed the team has landed and "they're heading to their residence safely".