The police statement said one of the last places he went to was a "city centre flat and from there he left to make his way to the Manchester Arena", where the attack took place.
Rowley, Britain's top counterterrorism police officer, said authorities have dismantled a "large part" of the network around bomber Salman Abedi.
British officials have confirmed he had recently returned from Libya and the officers said that police needed information about his movements since his return to Britain on May 18.
Of the 119 injured in Monday's attack, 66 remain in hospital and 23 of them are said to be in critical care.
"The intelligence services are still collecting information about him but I wouldn't rush to conclusions ... that they have somehow missed something", Ms Rudd said.
Police have issued a photograph of Abedi, a 22-year-old Briton born to Libyan parents, taken on Monday night before he blew himself up. Photos showed an army bomb-disposal unit at the property.
A huge bank holiday weekend security operation is under way as tens of thousands of people attend major spectacles including the FA Cup Final at Wembley and the Premiership Rugby Final at Twickenham. The stadium held a minute of silence for the bombing victims.
NEW YORK: Pop star Ariana Grande promised Friday to return to Manchester to play a charity concert following a suicide attack at her show, as she urged fans to respond to the tragedy with love.
"From midnight on Monday, there will be a well-planned and gradual withdrawal of members of the armed forces, who will return to normal duties", she said.
Former U.S. President Barack Obama offered his condolences to the victims and support for those wounded in the Manchester bombing during a meeting Saturday with Prince Harry at London's Kensington Palace. "We won't let this divide us".
In a statement released on Friday, she said: "I'll be returning to the incredibly courageous city of Manchester to spend time with my fans and to have a benefit concert in honor of and to raise money for the victims and their families".
"Our response to this violence must be to come closer together, to help each other, to love more, to sing louder and to live more kindly and generously then we did before".