"The public should be clear about what this means. A threat level of 'severe' means an attack is highly likely -- the country should remain vigilant," May said.
The decision to lower the threat rating from its highest level was made by the country's Joint Terrorism Analysis Centre in light of the arrests made in the Manchester attack investigation, May said. The level had been raised to "critical" after Monday's deadly bombing.
Investigators have identified the location where they believe the Manchester Arena explosive device was assembled, according to a statement from Greater Manchester Police late Saturday.
Police also released two still images of Abedi, taken from CCTV, on Monday evening, the night of the attack.
"We know one of the last places Abedi went was a city center flat and from there he left to make his way to the Manchester Arena," police said. "The flat is highly relevant as a location which we believe may be the final assembly place for the device."
Armed police are patrolling events in Manchester, London and elsewhere this weekend as Britain marks its first holiday since the bombing. But the deployment of soldiers on the streets in support of police will be phased out starting Monday night, May said.
Where will people see extra security?
In Manchester, events planned around the spring bank holiday will go ahead with additional security, including a significant number of armed officers, police said. British officers do not usually carry guns.
These include the Manchester Games, the Great Manchester Run, and a stadium show by bands including The Courteeners, all of which are likely to attract big crowds. This weekend also marks the start of Ramadan, the holiest month of the Muslim calendar.
"The change in the national threat level from 'critical' to 'severe' does not alter our response to Monday's horrific attack, which claimed so many innocent lives," Greater Manchester Police Chief Constable Ian Hopkins said.
Among high-profile events taking place in London are the FA Cup Final at Wembley Stadium, a major event on the soccer calendar, and a rugby final at Twickenham stadium. Chelsea Football Club canceled a Sunday parade to honor its Premier League victory.
London Mayor Sadiq Khan said enhanced security plans would remain in place in the capital this weekend despite the downgrading of the national threat level. Khan urged Londoners to remain vigilant, he said via Facebook.
Extra armed officers can patrol events this weekend because soldiers will guard key locations such as the Houses of Parliament, Downing Street and Buckingham Palace, said Chief Superintendent Jon Williams of London's Metropolitan Police Service.
"All of this is designed to make the policing approach unpredictable and to make London as hostile an environment as possible to terrorists," Williams said.
What's happened in the investigation?
Two more men were arrested early Saturday and taken into custody after officers raided a home in the Cheetham Hill area of central Manchester, police said in a statement. So far, 13 people have been arrested in the investigation, with 11 still in custody.
Police on Saturday also evacuated an area around a property in the Moss Side neighborhood of Manchester.
"The high pace and rapid progress of this investigation is continuing," said Britain's top counterterrorism officer, Assistant Commissioner Mark Rowley, adding that officers were gaining a greater understanding of how the bomb was prepared.
"There is still much more to do," he said. "There will be more arrests, and there will be more searches, but this greater clarity and this progress has led ... to the judgment that an attack is no longer imminent."
Military personnel will remain ready to deploy in support of the police if needed, even after they stand down, Rowley said.
UK authorities have disrupted five plots since March 22, when a terrorist attack outside Parliament in London left five people dead, Security Minister Ben Wallace said.
"There are over 400 investigations currently ongoing by the security services and police into terrorist planning or people thinking about terrorist planning," he said.
What about the Libya connection?
Abedi's younger brother said he knew generally about the plot
but did not know where and when the blast would be, a Libyan militia spokesman told private broadcaster Libya's Channel on Thursday.
Hashim Ramadan Abu Qassem al-Abedi spoke by phone with his brother Salman 15 minutes before the blast, the spokesman said.
The bomber's brother was detained in Libya a day after the bombing by a militia nominally under the control of Libya's interior ministry. The militia also arrested the brothers' father, Ramadan al-Abedi.
What about the victims?
All 22 of those killed in the bomb attack at the Manchester Arena concert have now been named
. Many were children, including an 8-year-old girl. Others were parents waiting to pick up their children from what was for many their first concert.
Family and friends have paid moving tributes to those lost. Dozens more were wounded, and as of Thursday, 23 survivors were in critical care in Manchester hospitals. Many suffered "horrific" and potentially life-changing injuries, a senior doctor said.
Grande posted a letter Friday on Twitter saying she would return to Manchester to perform a concert to raise money for the victims of the bombing and their families.
"The compassion, kindness, love, strength and oneness that you've shown one another this past week is the exact opposite of the heinous intentions it must take to pull off something as evil as what happened Monday," she said.
What's the mood in Manchester?
Politicians of all stripes have praised the people of Manchester for their spirit of unity and resilience in the wake of the attack.
Banks of flowers and balloons have been left in a city center square in tribute to the victims, and residents have joined vigils in their memory.
However, there is a darker side to life in the city in the wake of the bombing. Reports of hate crimes have spiked, from 28 -- a typical number -- on Monday to 56 on Wednesday, police said.
These can't be directly linked to Monday's bombing, Hopkins said, but police are monitoring the situation.