Prime Minister Boris Johnson will host an emergency Cobra meeting on Monday afternoon in response to the incident.
Assistant Chief Constable Russ Jackson, from Counter-Terrorism Policing North West, said the man who died in the blast brought a homemade bomb with him into a taxi and asked to be taken to the hospital.
He was picked up in the Rutland Avenue area of the city, and as the car reached the hospital’s passenger drop-off point, it exploded.
So far, four men have been arrested under terrorism laws in the Kensington area of Liverpool – three aged 21, 26, and 29, who were held on Sunday, and a man aged 20, who was detained on Monday.
The driver of the cab, named locally as David Perry, was treated in hospital after fleeing the car just before it burst into flames and has now been discharged.
Speaking to journalists at Merseyside Police headquarters, Mr Jackson said: “It is not clear what the motivation for this incident is.
“Our inquiries indicate that an improvised explosive device has been manufactured, and our assumption so far is that the passenger built this in the taxi.
Officers are searching two addresses – one in Sutcliffe Street and a second at Rutland Avenue in Sefton Park, where “significant items” have been found.
A cordon is in place, and eight families have been evacuated as a result.
Investigators have “attributed” the passenger to both the addresses but investigators are not yet sure where he lived.
They are looking into his associates, telephone records, and purchases he may have made.
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