One, who was arrested in the town of Wigan, 27 kilometres to the west of Manchester, had been carrying a package that was being "assessed".
Police on Tuesday raided Abedi's house in Manchester, using a controlled explosion to blast down the door.
"I think it's very clear that it's a network that we are dealing with", Chief Constable Ian Hopkins said on Wednesday afternoon.
Britain's top anti-terrorism officer Mark Rowley said events would only go ahead when it was safe to do so and the decision to raise the threat level had been made on a "precautionary basis" due to gaps in police knowledge while the investigation continues.
Ariana Grande has suspended several upcoming tour dates following the suicide attack at her concert in Manchester, England, Monday night that claimed the lives of 22 people.
A man in connection with the Manchester bombing attack has been arrested, according to a police statement released on late Wednesday.
Meanwhile French interior minister Gerard Collomb said security services in the United Kingdom and France have intelligence that suggest Abedi travelled to Syria.
France's interior minister Gerard Collomb told French television that both British and French intelligence services had information that Abedi had been in Syria.
Meghan Markle arrives as Prince Harry's date for Pippa Middleton's wedding reception
Markle arrived in London for the event a few days ago, leading many to hope that she would make an appearance at the nuptials. The little sister of Duchess Catherine wore the same gorgeous earrings she wore to Kate's 2011 wedding to Prince William .
Suicide bomber Abedi was born in Britain to a Libyan family, grew up in Manchester's southern suburbs and once attended Salford University there.
United States news site Politico reports both Ismail and Salman were known to British security services but neither had a criminal record.
Rudd had earlier scolded United States officials for leaking details.
Adam Schiff, the ranking Democrat on the House intelligence committee, told reporters on Wednesday he understands the concern about USA leaks possibly harming the United Kingdom police operation.
"Whilst some of what we are doing will be obvious to the public there is a huge amount of work happening day and night that the public will never know about", Commander Jane Connors, leading the London policing operation, said.
The Manchester bombing raised concern across Europe. A 23-year-old man was arrested in the south of the city yesterday.
Following the attack, almost 1,000 are now being deployed on Britain's streets to support police, as the United Kingdom remains on its highest terror alert amid fears of another attack.
Kuwaiti customs seizes pigeon with suspected drugs attached to its back
According to the Arab news service Al Arabiya , investigators had been tracking the pigeon, which was caught flying from Iraq. Homing pigeons have been used in the pass to carry messages, and have crossed a distance of approximately 100 miles.
"The investigation into the terrorist attack in Manchester is large-scale, fast-moving and making good progress", Rowley said.
Rudd said up to 3,800 soldiers could be deployed on Britain's streets, taking on guard duties to free up police to focus on patrols and investigation. An initial deployment of 984 had been ordered, first in London and then elsewhere.
"Right now, her main headspace and focus is the victims and how she can help".
She also complained about USA officials leaking sensitive information about Abedi to the press, saying that could hinder Britain's security services and police.
In addition to those killed in the concert attack, 64 people are being treated for their wounds, Jon Rouse of the Greater Manchester Health and Social Care Partnership said Wednesday.
"The London O2 shows this week have been cancelled as well as all shows through June 5 in Switzerland".
Chelsea soccer club said it had cancelled a victory parade that had been set to take place on Sunday to celebrate its Premier League title. The Champions Trophy begins on June 2.
Ms Rudd said she had told Washington "it should not happen again".
Roger Ailes hit his head one week before he died
The man responsible for turning Fox into a conservative media force resigned last summer amid allegations of sexual harassment . Bush tweeted that while his "friend" Ailes "wasn't flawless ", he may not have been elected president without him.
Whitehall officials are said to be "furious" after details and pictures connected to the probe continued to appear in the American media against the Home Secretary's instructions. They said they would formally name the victims after forensic post-mortems, which would take four or five days.
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