In addition to those killed in the concert bombing, Manchester officials raised to 119 the number of people who sought medical treatment after the attack.
The senior British government official said May would say that she believes "we must redouble our resolve to meet the threats to our shared society whether from terrorism or Russia".
The group continues to have a presence in the country, which US counterterrorism official, Nicholas J. Rasmussen, told The New York Times caused the government to be "very concerned", particularly over fighters who could continue to maintain a foothold in the unstable country.
A Muslim community worker, who did not want to be identified, has told the BBC that two people, who knew Abedi at college, made separate calls to a hotline to warn the police about his extremist views.
Police said they were working to establish whether Abedi - who blew himself up in the attack outside Manchester Arena, killing 22 people, including children, and injuring 59 others - was working alone or as part of a group.
Rudd also said Abedi had been known to security services before the bombing.
The decision to allow the North Atlantic Treaty Organization to join the coalition against Islamic State in Syria and Iraq follows weeks of pressure on the two allies, who are wary of NATO confronting Russian Federation in Syria and of alienating Arab countries who see NATO as pushing a pro-Western agenda.
Mr Kinsey said an Asian man in his mid 20s, who wore mainly Islamic clothes, appeared to have been living in the house alone for the a year ago but had lots of visitors.
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Officials are probing how often Abedi had travelled to Libya, which has seen an eruption of armed Islamist groups since dictator Moammar Gadhafi was overthrown and killed in 2011.
The Manchester bombing has raised concern across Europe.
Mrs May said soldiers were being placed at Buckingham Palace, Downing Street, embassies and the Palace of Westminster to support armed police in protecting the public.
Armed officers raided an address in the Fallowfield area, where Abedi, believed to be Libyan but British-born, was registered as living, and carried out a controlled explosion.
In France, Interior Minister Gerard Collomb said Wednesday that British and French intelligence had information that Abedi most likely traveled to Syria. At another property, a house a 10-minute walk from where Abedi lived, neighbours said they were awakened by a loud noise and saw a man hauled away in handcuffs. Armed police patrolled outside St. Paul's Cathedral in London, another popular tourist spot.
Asked whether the USA leaks had compromised the investigation, she said: "I wouldn't go that far but I can say that they are perfectly clear about the situation and that it shouldn't happen again".
Still, their stories began to emerge: Michelle Kiss, a mother of three whose "family was her life;" Nell Jones, an "always smiling" teenager; Martyn Hett, who packed life "to the brim with his passions;" Jane Tweddle, a "bubbly, kind, welcoming" receptionist.
"Focusing on counter terrorism is not just about the military defeat of terrorists but addressing the root causes of terrorism and the propagation of poisonous ideology particularly online", the official said. Officials say 20 of them are being treated for critical injuries.