The 19-year-old was arrested in north London on Friday, a day after the device was blown up in a controlled explosion at North Greenwich station.
Westminster magistrates say he can now be detained until 12:20 BST on Friday.
Searches are continuing at a house in Newton Abbot, Devon, but police say a device found there was "not viable".
Homes were evacuated and a 200m (650ft) cordon set up after the device was found at the house in Tudor Road earlier. The cordon has since been removed.
The Newton Abbot device was found by officers from the Metropolitan Police's counter-terrorism command, as they searched the property on Saturday afternoon.
After the device was declared non-viable, Devon and Cornwall Police said further forensic searches would continue at the house and a police guard would remain in place.
Meanwhile, the Metropolitan Police says security has been stepped up around the transport network in London.
Passengers have been told to expect to see more officers, including armed police, in and around transport hubs, while patrols by British Transport Police are in place on the Underground and at railway stations.
Scotland Yard said the Greenwich device was being examined.
The Met said officers were keeping an open mind regarding any possible motive but said they were not looking for anyone else in relation to the investigation at this stage.
The device destroyed at North Greenwich on Thursday was reported to have been found on an eastbound Jubilee Line train and handed to the Tube driver.
The driver treated it as a suspicious and said it contained "wires and possibly a clock".
The station was evacuated and members of the Met's bomb squad carried out the explosion, after the item was described as looking "real enough".
The 19-year-old man was held in Holloway Road, north London, on Friday. A Taser was used during his arrest.
The current threat level for international terrorism in the UK is severe - meaning an attack is deemed to be "highly likely".
Counter-terror police investigating the discovery of a suspicious item on a Tube train have been granted a warrant to hold a man for further questioning.