Mark Rowley, Assistant Commissioner for Specialist Operations in the Metropolitan Police Service, said detectives had made "immense progress" in the investigation, but warned there were still "important lines of inquiry" to pursue.
"Further arrests are likely, although police believe they have got hold of a large part of the network," Rowley said.
He said police have reviewed security at more than 1,300 events across the UK and urged public not to change any plan and "go out as you planned and enjoy yourselves".
Greater Manchester Police said the man was taken into custody after a property search at an address in the Moss Side area of Manchester.
With the new arrest, the number of people arrested reached 10, of which two have been released without charge, police said.
"Eight men remain in custody for questioning," a police statement said.
A 16-year-old boy and a 34-year-old woman were the two persons released without charge.
The other eight men, aged between 18 and 38, were being questioned over their involvement in the attack and are expected to be charged soon.
Rowley said: "Broadly speaking, as with any investigation of this nature, we are focusing on understanding Abedi's life; forensically examining a number of scenes, reviewing hours of CCTV from the night itself and the hours and before, financial work, communication, digital exhibits, the accounts from hundreds of witnesses and of course enquiries internationally."
Some news reports indicated that security forces were on the hunt for a second device made by Abedi, which may now be with a member of this network.
In the Libyan capital Tripoli, Abedi's younger brother 20-year-old Hashem and their father, Ramadan, are 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.
Elwafi is believed to have handed himself to police after news reports revealed Abedi as the suicide bomber.
The UK terror threat level remains "critical", meaning another attack could be imminent and additional Army and armed police officers are patrolling major sites, including the transport network, across the UK.
Britain's Home Secretary Amber Rudd chaired another Cabinet Office Briefing Room A (Cobra) meeting today.
"JTAC (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," said Rudd.
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.
US Secretary of State Rex Tillerson met UK foreign secretary Boris Johnson in London today and said the US took "full responsibility" for the leaks.
"This special relationship that exists between our two countries will certainly withstand this particular unfortunate event,"he said.
Meanwhile, the national-level campaigning for the June 8 general election resumed today after local level campaigns restarted yesterday, following suspension in the wake of the attack.
Opposition Labour party leader Jeremy Corbyn began the campaign with a major speech in London attacking the "war on terror".
He said, "Many experts, including professionals in our intelligence and security services, have pointed to the connections between wars our government has supported or fought in other countries and terrorism here at home.
"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."
She used her speech there to urge world leaders to do more to combat online extremism.
"The fight is moving from the battlefield to the internet," she said.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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