London Fire Brigade requested that parts of the Circle and Hammersmith and City line be closed.
"The Brigade advised that a section of track be temporarily closed due to the short term risk of some debris from the tower falling onto the track," a London Fire Brigade spokeswoman said.
"Specialist urban search and rescue teams are currently securing loose debris right now so the station can open again."
The track in question is above ground and lies a stone's throw away from Grenfell Tower, where at least 30 people died on Wednesday after a fire engulfed the building.
"No service between Edgware Road and Hammersmith due to the recent fire in the Latimer Road area," said a tweet on the account of the Circle Line. The Hammersmith and City line, which runs along the same track and stops in that part of west London, was also partially suspended.
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