A 25-year-old man and a 19-year-old man have been arrested on suspicion of terror offences, Greater Manchester Police has said.
Officers investigating the Manchester Arena attack are also searching an address in Moss Side, the force said.
Thirteen people are now being held in custody after the suicide bombing at the Manchester Arena left 22 dead.
Investigators are working to identify potential members of a terror network that could have given support to suicide bomber Salman Abedi.
On The Andrew Marr Show, Home Secretary Amber Rudd said MI5 was looking at around 20,000 separate plots and tip-offs relating to terrorism.
She also said the security services could be allocated more funding if necessary.
Meanwhile, police have released CCTV stills of Abedi in a plea for new information about his movements between 18 May and Monday’s attack.
Earlier, thousands took to the streets for the Great Manchester Run as the latest large-scale event took place in the city in the wake of the terror attack.
Armed police mingled with spectators as crowds gathered to watch the runners, including mayor of Greater Manchester Andy Burnham.
Burnham said going ahead with the event, which included a half marathon and the 10k he was running in, was a difficult decision.
He said it had to happen in order not to hand a victory to terrorists.
Participants including comedian John Bishop and former England and Manchester United captain Bryan Robson stood on the 10k start line under the banner #RunForManchester, many wearing yellow ribbons in solidarity with the victims of the Manchester Arena attack and their families.
Police officers from Wales were among those helping out as a heightened security operation remained in place.