With the new arrest this morning from an inner-city area in Manchester, the number of people arrested reached 10, of which two have been released without charge, police said.
"Eight men remain in custody for questioning," they said.
A 16-year-old boy and a 34-year-old woman were the two person released. The other eight men, aged between 18 and 38, were being questioned over their involvement in the attack on Monday that killed 22 people, the police said in a statement.
Abedi was known to UK security services, but his risk to the public remained "subject to review", according to reports.
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In the Libyan capital Tripoli, Abedi's younger brother 20-year-old Hashem and their father, Ramadan, were being held by special forces linked to the country's interior ministry.
Meanwhile, the manager of a pizza shop raided by police in north England claimed that his friend Aimen Elwafi was one of the eight men in custody as he had inadvertently rented a property to Abedi.
"He made the connection straight away. He was shocked and panicked when he saw the news," said Mohammed El-Haduri, the manager of St Helens Pizza.
The suicide attack at American pop star Ariana Grande's concert had sent shockwaves across the UK, prompting back-to- back meetings of the emergency response Cobra committee.
After the meeting, Prime Minister Theresa May announced the threat level has been raised to the highest "critical", meaning another attack could be imminent. Army and armed police officers patrolled major sites across the country.
"[Joint Terrorism Analysis Centre] have assessed that the level of threat should remain at critical while the operation continues. The military are continuing to support the police under Operation Temperer - 1,000 members of the military are assisting in that," she said.
Sixty six people injured in the attack were still in hospital, she added.
British police have now resumed intelligence-sharing with their US counterparts after a brief suspension over a series of leaks by American officials to journalists providing details of the Manchester bomb investigation.
"This special relationship that exists between our two countries will certainly withstand this particular unfortunate event," he said.
US President Donald Trump earlier said the leaks were "deeply troubling".
Meanwhile, national level campaigning for the June 8 general election resumed today after local level campaigns were resumed yesterday following suspension in the wake of the attacks on Monday night.
Opposition Labour party leader Jeremy Corbyn began with a major speech in London attacking the "war on terror".
"We must be brave enough to admit that the 'war on terror' is simply not working. We need a smarter way to reduce the threat from countries that nurture terrorists and generate terrorism."
The ruling Conservatives, who criticised his speech as "crassly timed", have had a relatively low-key campaign today with British Prime Minister Theresa May in Sicily to attend a G7 Summit meeting.
She used her speech there to urge world leaders to do more to combat online extremism.