Police are questioning two brothers - one of whom was shot during a raid - on suspicion of terrorism involvement.
Muhammad Abdul Bari called for clarity from police
Following the raid on Friday officers waited until Monday for the shot man - Mohammed Abdulkahar, 23 - to recover enough to be interviewed.
Mr Abdulkahar and his brother, Abul Koyair, 20, both deny the allegations.
Muslim leader Muhammad Abdul Bari has warned trust between Muslims and police could be damaged in the wake of the raid in Forest Gate, east London.
Assistant Commissioner Andy Hayman has said they had "no choice" but to carry out the raid after getting "specific intelligence".
Mr Abdulkahar was treated in hospital for a wounded shoulder after the raid.
He was then transferred to Paddington Green high security police station, and on Monday afternoon doctors said he had recovered enough for questioning.
Both brothers are being questioned about involvement in planning or carrying out terrorism acts.
Police expect to ask magistrates on Wednesday for permission to continue holding the men for up to 14 days.
On Tuesday evening, Mr Koyair's solicitor Julian Young emerged from Paddington Green police station to issue a statement on behalf of his client.
He said: "I still maintain that I am completely innocent of any acts to do with terrorism.
"I am OK and keeping strong. My family need not worry about me."
The solicitor confirmed that the police would be seeking two extensions to hold the brothers in custody for a further period of time.
Recently-elected Muslim Council (MCB) of Britain leader Muhammad Abdul Bari urged police to give a "clear picture" of the operation.
Dr Bari visited Forest Gate to listen to the "evident concerns" of Muslims in the area.
"The danger is the trust between the community and the police may be broken. The community feels very vulnerable," he said.
He said this was a "crucial time" for the Muslim community.
"People want to know what exactly happened and about the intelligence - is it genuine information, is it flawed - these are the questions police have to answer as soon as possible."
Police said "specific intelligence" prompted them to raid the house, looking for a chemical device - which they have yet to find, although documents and computers have been removed for analysis.
They said the search of the terraced house in Lansdown Road could continue until the end of the week.
Dr Bari said the search should be speeded up because "three or four days' frustration, confusion and anger in the community is not good".
"Trust could be an issue. Trust could break down if things are not clarified as soon as possible."
A former chairman of the Joint Intelligence Committee, Paul Lever, said police had to act on information they received.
"Intelligence virtually never gives you 100% confidence or certainty.
"It gives you perhaps grounds for suspicion and in the circumstances that sadly we're now in, the penalty of not taking action if you have some grounds for suspicion is potentially horrendous and that's the dilemma that the security service and the police face," he said.
Mr Abdulkahar's solicitor Kate Roxburgh has said her client was shot by an officer at close range as he came down a flight of stairs.
The shooting is being investigated by the Independent Police Complaints Commission.