Three people were arrested - and quickly de-arrested - during the afternoon's operation at Quantock Street, Moss Side, leading them to post an outraged sign on their front door.
"I believe we can get them to be more successful in working with us to find a way of getting some of that information".
About 1,000 armed police officers have been freed up by a decision to deploy the Army to protect key sites including Buckingham Palace and the Houses of Parliament under Operation Temperer.
Britain's security level has been upgraded to "critical" meaning officials believe another attack may be imminent.
Hospitals have been warned to be ready.
The opposition Labour Party, emboldened by a rise in opinion polls, argued that Britain's foreign policy had increased the risk of attacks and criticised Conservative Prime Minister Theresa May for cutting spending on policing.
"What we are doing is challenging the people who are delivering end-to-end encryption to work with us so that we have a way of keeping people safe", she said.
Ms May hit back: "Jeremy Corbyn has said that terror attacks are our own fault".
May was speaking to reporters at a summit of Group of Seven leaders in Sicily where she won support for action to prevent militants from using the internet to spread propaganda. Britain's top counter-terrorism officer Mark Rowley said that while there were still important lines of inquiry to pursue and further arrests were likely, the public should "go out as you planned and enjoy yourselves" over the bank holiday weekend.More news: Cleveland Cavaliers fans flock to stores for Finals merchandise
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Among those in custody is Abedi's brother Ismail, who was arrested in Whalley Range, south Manchester, on Tuesday.
Almost 23,000 terror suspects may be at large across Britain, the country's intelligence community say after the deadly Manchester attack by a Libyan-origin man who was on the radar of the UK's spy agencies.
Police have said they have arrested a large part of the network behind the bombingwhich killed 22 people at a concert hall. Buildings across Manchester and northwest England were raided.
U.S. Secretary of State Rex Tillerson says the United States takes "full responsibility" for the leaking of information from Britain's investigation of the Manchester concert bombing.
At a press conference at the G7 summit in Sicily on Friday, Mrs May said: "Yes, I did raise the issue of leaks of information that have been shared by the police with the Federal Bureau of Investigation with President Trump".
Tillerson said Friday that the "special relationship that exists between our two countries will certainly withstand this particular unfortunate event".
The 36-year-old said: "This is my home town".
"Our response to this violence must be to come closer together, to help each other, to love more, to sing louder and to live more kindly and generously than we did before", she said.
"We can't directly link these to the events of Monday night and are continuing to monitor the situation", he said.