The statement read: "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".
Videos shared on social media appeared to show an aeroplane which posters identified as the Saudi team's aircraft with its wing on fire while it was in the air.
The aircraft landed with both of its engines working and the passengers disembarked normally, the agency's statement said. Airline Rossiya have leased the plane since April 2016.
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"No warning was sounded during the landing at Rostov-on-Don airport".
A Saudi Arabia statement said: "All the Saudi national team players have arrived safely and now are staying in their residence".
In their final game of the group, they take on Egypt, who play Russian Federation on Tuesday.
Tabarez confirmed that he will reward the evergreen wingers with starting berths against Saudi Arabia, the second lowest ranked team in the tournament who were thrashed 5-0 by Russian Federation in their opener.