Ms Smith told BBC One's Andrew Marr programme: "There have been a lot of charges thrown around here - the idea that, you know, this is Stalinism, this is a police state.
"In my book, Stalinism and a police state happens when ministers direct and interfere with specific investigations that the police are carrying out."
Ms Smith, who also declined to condemn the fact police searched Mr Green's office in the House of Commons, said the leak investigation was launched at the request of the Cabinet Office and the head civil servant at the Home Office, and not by her.
She added that the leaks in the public domain were not necessarily all the things which formed the "systematic series of leaks... breaches of security" which were being investigated.
'Implausible or incompetent'
Pressed about what she knew when, Ms Smith said she had known there was a leak inquiry going on and knew in advance that a Home Office official was being arrested as part of it on 11 November.
Conservative leader David Cameron, writing in the News of the World, challenged ministers to condemn the arrest and said the prime minister's stance so far was "not good enough".
He said: "The question is: does he think it is right for an MP who has apparently done nothing to breach our national security - and everything to inform the public of information they're entitled to know - to have his home and office searched by a dozen counter-terrorist police officers, his phone, blackberry and computers confiscated, and to be arrested and held for nine hours?"
There is no crime, this is an abuse of police powers, this is President Nixon's America - harassing a political opponent of the government. It should stop
Lib Dem leader Nick Clegg told the same BBC programme the claim Ms Smith did not know the arrest was looming was either "implausible" or showed "incompetence".
The incident has also angered MPs within the Labour Party. David Winnick - a Labour member of the home affairs select committee - said he wanted an "immediate statement" from the minister when Parliament resumes on Wednesday.
He said the search of Damien Green's Commons office was a serious breach of parliamentary privilege.
The Independent on Sunday has separately reported that offices of senior Tories, including Mr Green, were routinely swept for electronic bugging devices as they feared they were being spied on.
Ms Smith said that she had not signed any warrant to approve the bugging of Mr Green.
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