The country's top counter-terrorism officer suggested on Friday night that more than one suspect could have been involved in the attempt to slaughter commuters in a tube carriage.
Assistant Commissioner Mark Rowley said police were "chasing down suspects", while suggestions were made by Donald Trump that the bomber was known to Scotland Yard.
Security Minister Ben Wallace told the BBC on Saturday: "We haven't been able at the moment to catch the bomber. The bomber is still out there - or bombers - and we have to get to the bottom of that and follow up the leads."
The improvised device - reportedly containing the explosive triacetone triperoxide (TATP) and packed with nails - was dumped on a busy District Line train during Friday rush hour.
Its detonation from inside a bucket, which is thought to have only been partial, injured 29 people.
Parsons Green station was re-opened in the early hours of Saturday, shortly after the Prime Minister announced the Joint Terrorism Analysis Centre set the terror threat at its highest level.
It was the second time this year the country was placed at "critical", meaning an attack "may be imminent", the Prime Minister said - the other occasion being the Manchester Arena bombing which killed 22 people in May.