Soldiers deployed to support the police will be stood down on Monday night, at the close of the bank holiday weekend.
Earlier on Saturday, police evacuated an area of Moss Side in the city, in a search linked to Monday's bomb attack at the Manchester Arena which killed 22 people and left scores injured.
The evacuation was described by Greater Manchester Police as a precautionary measure to "ensure everyone's safety".
Mrs May made the announcement after leading a meeting of the government's emergency committee Cobra on Saturday morning.
She said significant activity by the police during the last 24 hours had led to the threat being reduced.
It had been set at critical in the aftermath of the bombing.
There will be "more arrests and more searches" linked to the Manchester attack, the UK's most senior counter-terror officer Mark Rowley said following Mrs May's announcement.
"We are getting a greater understanding of the preparation of the bomb," he said. "There is still much more to do."
Greater Manchester Police said the change in threat level had not altered its response to Monday's attack.
Chief Constable Ian Hopkins said: "The level of resources we have available to us remains the same as we continue to take positive action."
Detectives are questioning 11 men about the attack following a series of raids.
In the latest arrests, police held two men, aged 20 and 22, after carrying out a controlled explosion at an address in the Cheetham Hill area of Manchester early on Saturday.
There were also searches at a separate property in Cheetham Hill and in the Longsight area.
Armed police are guarding hundreds of events across the UK at the start of the bank holiday weekend.
Police reviewed security at more than 1,300 events across the country, and say people can be "100% confident" they are doing everything possible to protect them.
Senior officers have encouraged people to go out but to remain vigilant.
Security has been increased at Wembley for the FA Cup Final, Hampden Park for the Scottish Cup Final, Twickenham for the Aviva Premiership Rugby Final, and for the Great Manchester Run on Sunday.
Hundreds of police are on duty at Lancashire Cricket Club's Old Trafford ground, which is hosting 50,000 music fans on Saturday evening.
The concert, headlined by Manchester-based band The Courteeners, is the first major music event in the city since the bombing.
Among the entertainment, sporting and community events taking place is Radio 1's Big Weekend in Hull.
Music briefly stopped on all three stages at 15:00 BST on Saturday as a minute's silence was held at the event in East Yorkshire in honour of those killed and injured in the Manchester attack.
Minute silences have also been held at sporting events including football's Scottish Cup final and rugby union's Premiership final.
Seven children were among those who died when Salman Abedi, 22, detonated a bomb at the Manchester Arena on Monday night, at the end of a concert by US singer Ariana Grande.
NHS England said 116 people had received inpatient care, with 63 still in hospital - including 20 in critical care.
More about: #Manchesterarenaattack #TheresaMay
