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Jomo Kenyatta International Airport (JKIA) - a key regional hub - has been closed, passengers evacuated and incoming flights diverted reported by BBC.
The fire is now said to have been contained but there have been reports that it took emergency services a long time to respond.
Images from the scene showed flames leaping from one of the main buildings.
There have been no reports of any casualties and the cause of the fire is not clear.
James Ole Lenku: "We will make sure that we establish the true cause of the fire. As of now we don't know what's happened"
Jomo Kenyatta International Airport is the regional hub for East Africa, with many long-distance flights landing there to connect to countries across the region.
The airport is the main gateway for European tourists - and it is now the height of the tourist season - and is also crucial for the country's key flower export industry, so the fire could have a huge economic impact, says the BBC's Emmanuel Igunza at the scene.
Shares in Kenya Airways fell in early trading on Wednesday.
Despite earlier official statements that the airport had been closed indefinitely, presidential spokesman Manoah Esipisu said domestic flights and international cargo flights would resume later on Wednesday.
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