Police said they were "chasing down suspects" and had hundreds of officers trawling CCTV in the wake of the District Line attack, which injured 29.
The UK terror threat has been raised to critical - the highest level - meaning an attack may be imminent.
So-called Islamic State has said it was behind the bomb, which was detonated at 08:20 BST at Parsons Green station.
The station reopened in the early hours of Saturday.
The Met's Assistant Commissioner Mark Rowley said it was "very routine" for IS to claim the attack "whether or not they've had any previous engagement with the individuals involved".
He asked the public to remain "vigilant", but said people should "not be alarmed".
Announcing the change in the UK threat level, Prime Minister Theresa May said the military would be providing support to police and would replace officers on guard duty at national infrastructure sites that are not accessible to the public.
The use of the military to assist police is part of 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."
Passengers described the bomb, which was in a supermarket carrier bag, as a "fireball".
Patients were taken to four London hospitals, including one with a specialist burns unit.
It is understood the device had a timer but the BBC's 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.
Police urged anyone who took pictures or videos at the scene to upload them to ukpoliceimage