Home Secretary Jacqui Smith denied that ministers had been involved in any way in the arrest of Mr Green.
"The Metropolitan Police have been completely clear that that arrest happened without either ministerial involvement or authorisation," she said.
Both the Conservatives and Liberal Democrats condemned Mr Green's arrest and search of his parliamentary office, by nine members of the Met's counter-terrorism squad.
Describing the operation as "heavy handed", Tory leader David Cameron said: "If they wanted to talk to Damian Green why not pick up the telephone and ask to talk to him."
"[The police] have got questions to answer, frankly, I think government ministers have got questions to answer as well. If they didn't know, why weren't they told?
"As far as I can see, he made public some information that was in the public interest that the government found uncomfortable."
Lib Dem leader Nick Clegg told the BBC that he was "really shocked" by Mr Green's arrest.
"This is something you might expect from a tin-pot dictatorship, not in a modern democracy," he said.
Nick Clegg said the arrest was a "mayday warning" for democracy in Britain
Given the culture of "extraordinary secrecy" in Whitehall, it was getting harder to hold the government to account and opposition MPs had a constitutional duty to keep "ministers on their toes", he added.
He called on Gordon Brown to "rule out any further use of anti-terrorism powers in cases that have nothing to do with terrorism."
The Metropolitan Police said the arrest was made under the Police and Criminal Evidence Act, rather than anti-terror legislation.
BBC political correspondent Carole Walker said the Speaker of the House of Commons, Michael Martin, was also under pressure to justify why he had allowed police to enter Parliament and search Mr Green's office.
A spokeswoman for the speaker said: "There is a process to be followed and that was followed."
There was also concern on the Labour benches.
Former minister Denis MacShane said that the Speaker should make clear that MPs were entitled to hold sensitive material in the same way as lawyers and doctors.
"To send a squad of counter terrorist officers to arrest an MP shows the growing police contempt for Parliament and democratic politics," he said.
"The police now believe that MPs are so reduced in public status that they are fair game for over-excited officers to order dawn raids, arrests and searches of confidential files held by MPs or those who work for them.
"I am not sure this is good for British democracy."
According to the Home Office, no ministers were told about the raids in advance.
However, Mr Cameron, London mayor Boris Johnson, and Commons Speaker Michael Martin were all given prior notice.
The decision to make today's arrest was taken solely by the MPS without any ministerial knowledge or approval
Former Conservative Home Secretary and Tory leader, Michael Howard, said he would be "astonished" if he had not been told about the police investigation when in office.
"I would have expected to be told. This was an investigation we know initiated by the Home Office. Are we to believe that nobody in the Home Office was told?"
He added: "If nobody knew it tells you something about the way government is working at the present time, and about the relations between ministers and senior civil servants."
Mr Green was not charged with any offence but was released on bail until February, when he could face further questioning.
The Ashford MP, the Tories' immigration spokesman since 2005, has denied any wrongdoing and said "opposition politicians have a duty to hold the government to account".
Damian Green: "I emphatically deny I did anything wrong"
The Met said some counter-terrorism officers were involved in the arrest because they were the most "appropriate" to carry out such an operation.
Shadow Home Secretary Dominic Grieve has released a list of more than 50 questions he said the government had to answer about the arrest, including when ministers and officials were told about it.
"The government's limp and confused response begs more questions than it answers. Ministers have some very important questions to answer."
Sir David Normington, the top civil servant at the Home Office, said he had taken the decision to ask for police help in identifying the source of a series of "leaks of sensitive information over an extended period," because the leaks had "risked undermining the effective operation of my department".
"The police investigation led to a junior member of the Home Office being arrested on 19 November and subsequently suspended from duty," said Sir David in a statement.
Home Office leaks
"Yesterday (Thursday), I was informed by the Metropolitan Police at about 1.45pm that a search was about to be conducted of the home and offices of a member of the Opposition front bench. I was subsequently told that an arrest had been made.
"Ministers were not involved in the decision to seek police assistance or in the subsequent investigation and were only told of the arrest after it had occurred."
The leaks thought to be at the centre of the investigation include:
The November 2007 revelation that the home secretary knew the Security Industry Authority had granted licences to 5,000 illegal workers, but decided not to publicise it.
The February 2008 news that an illegal immigrant had been employed as a cleaner in the House of Commons.
A whips' list of potential Labour rebels in the vote on plans to increase the pre-charge terror detention limit to 42 days.
A letter from the home secretary warning that a recession could lead to a rise in crime.
The Metropolitan Police confirmed Mr Green was arrested by members of its counter-terrorism command, thought to be Special Branch officers, at his home in Kent and searches were conducted at his homes in London and Kent and at two offices in Kent and London.
It said the investigation was not terrorism related but did fall within the counter-terror unit's remit and that it was made without the knowledge or approval of ministers.
Police say Mr Green was held on suspicion of "conspiring to commit misconduct in a public office" and "aiding and abetting, counselling or procuring misconduct in a public office" - an obscure and little-used offence under common law.
One legal expert said it was doubtful whether any case would be brought against Mr Green.
"In a western democracy, I think it would be very surprising if an elected member of Parliament was put on trial for an offence which arises from him putting in the public domain material that he thinks should be there in the public interest," said Robert Brown, a partner at the law firm Corker Binning.
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