Police examined a house in West Midlands as part of the operation
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Ten people suspected of terrorism are continuing to be questioned by police.
The Home Office and police have refused to comment on newspaper reports the 10 were planning to carry out suicide bombings in Manchester.
The nine men and one woman were arrested on Monday after 400 police were involved in raids.
Representatives of both Manchester United and Manchester City have denied speculation their grounds may have been specifically targeted.
Those arrested are being held under the Terrorism Act on suspicion of involvement in the commission, preparation or instigation of terrorism.
Six men and the woman were arrested in Manchester, and one person each in Staffordshire, West Midlands and South Yorkshire.
Security services and the Metropolitan police anti-terrorism branch were also involved in the operation.
Greater Manchester Police said speculation that public buildings in Manchester were targets for terrorists was "extremely unhelpful" and urged the public to be vigilant.
Newspapers reported on Tuesday that police were investigating plots to launch suicide attacks, possibly at Manchester United's Old Trafford ground and their rival's City of Manchester Stadium and the Trafford Centre shopping complex.
But both football clubs and the shopping centre said they had not been specifically targeted.
Manchester United director of communications Phil Townsend told BBC Five Live Breakfast: "Old Trafford has not been identified as a target.
"We are always in discussions with police, but not specifically about being a terrorist target."
He added that there were "no additional measures in place for tonight's game" when Manchester United play Charlton.
Manchester City chairman John Wardle also told Five Live that no specific discussions had taken place with police regarding their stadium being a terrorist target.
The arrested people were of north African and Iraqi Kurdish origin, Assistant Chief Constable David Whatton of Greater Manchester Police told BBC News.
The suspects can be held for questioning for 14 days without charge.
He described the arrests and searches as "part of an ongoing operation looking at the threat of terrorism across the whole of the United Kingdom".
He said it would also continue in the future, but
"it is something the public has become aware of as we have done some overt activity".
"This is working against the background that we've never had a such a high level of threat from terrorism in the United Kingdom since some time before Christmas," ACC Whatton said.
A Home Office spokesman said it would be "inappropriate" to comment on police inquiries while they were ongoing.
He said: "We cannot get into a running commentary on the intelligence and information behind police and security services operations, as to do so would undermine counter-terrorist work.
"We have always said that we would not hesitate to issue a warning if it is the best way to protect the public in respect of a specific and credible threat."