The use of the military to assist police has been done under the first phase of Operation Temperer, a government plan to deploy troops to help police following major terrorist attacks, which was activated for the first time on 23 May following the Manchester Arena attack.
Mrs May said: «The public will see more armed police on the transport network and on our streets, providing extra protection.
«This is a proportionate and sensible step which will provide extra reassurance and protection while the investigation progresses.»
Twenty-nine people have been treated in hospitals, mostly for burns, following the attack at 08:20 BST on Friday on the eastbound District Line train from Wimbledon.
Assistant Commissioner Mark Rowley said police were «chasing down suspects».
He said the assistance from the military would «provide reassurance» across the country.
Mr Rowley said hundreds of police officers had been «trawling» through CCTV to find those responsible for the attack.
He said detectives were only aware of one device and refused to be drawn on details of the suspects because of the «covert» nature of the operation.
M Rowley also said it was «very routine» in incidents of this kind for IS to say it carried out the attack «whether or not they’ve had any previous engagement with the individuals involved».
What does terror threat level mean?
By Dominic Casciani, home affairs correspondent
A word of caution about «imminence».
The terror threat level was previously raised to critical in May after Manchester.
Then it was lowered again days later after it became clear to intelligence assessors in the Joint Terrorism Analysis Centre that an attack wasn’t imminent.
Then we had two more incidents – Borough Market/London Bridge and Finsbury Park.
What does this tell us?
Intelligence is usually fragmentary.
Analysts sometimes only have glimpses or impressions of what they think is going on.
It’s an imperfect world.
Pictures taken of the train showed a white bucket on fire inside a supermarket bag, with wires trailing on to the carriage floor. The BBC understands the device had a timer.
BBC security correspondent Frank Gardner said the bomb appeared not to have gone off properly.
Had it worked as intended, it would have killed everyone around it and maimed everyone in the train carriage for life, he said.