Officers had to be allowed to "follow the evidence where they need to" and it would be "Stalinist" for politicians to intervene, she told the BBC.
David Cameron has urged Gordon Brown to condemn the action against his immigration spokesman Damian Green, insisting he was simply doing his job of holding the Government to account.
But Ms Smith said the investigation was examining a "systematic series of leaks" of potentially sensitive material beyond the cases being claimed by critics.
"It is not an investigation into whether or not Opposition politicians used information they received to embarrass or hold to account the Government," she told BBC1's Andrew Marr Show.
"That is a completely legitimate activity it has gone on; it should go on; it will go on.
"This started as an investigation of a systematic series of leaks from a department that deals with some of the most sensitive and confidential information in government.
"There are four leaks that are in the public arena. The point is that this started as an investigation into a systematic series of leaks about which, of course, it was not clear what had been leaked and what may not have been leaked."
Repeating her insistence that she had not been aware a senior Tory was to be arrested until after it happened, she said: "What we appear to be being asked to do, by former home secretaries, by the Leader of the Opposition, is to intervene in a specific investigation being carried out by the police who I do believe, when they start an investigation, should, as they have said they need to, follow the evidence where they need to.
Replying to critics of the police action, she went on: "In my book Stalinism and a police state happens when ministers direct and interfere with specific investigations that the police are carrying out.
"I have been very clear that in my view the police should have operational independence, they should be able to pursue those investigations in the way in which their professional judgment suggests.
"I do not know what evidence they are looking at - neither do any of the other people who are commenting.
"If you believe in the principle of operational independence of policing, you believe in that even when they are difficult and sensitive investigations."
In an apparent reference to the cash-for-honours inquiry that engulfed Labour, she said: "Any police investigation that involves a senior political figure or elected representative, as incidentally we have seen in other investigations in recent years, is highly-sensitive and decisions need to be taken very carefully about it."
Ashford MP Mr Green was detained on Thursday and held and questioned for nine hours.
His homes and offices, including in the House of Commons, were searched and his computer, phone and other communications equipment seized in the raids.
It followed the earlier arrest and then suspension of a junior official, believed to be 26-year-old Chris Galley.
Scotland Yard said that 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".
The leaks are thought have included the disclosure that 5,000 illegal immigrants were working as security guards and bouncers; news that an illegal immigrant was employed as a cleaner in the House of Commons; a whip's list of potential Labour rebels against 42-day detention for terror suspects; and a letter from Ms Smith to Mr Brown warning that the recession would spark a rise in crime.
Amid mounting anger from all sides at Westminster, Mr Cameron accused the Prime Minister of hypocrisy for refusing to speak out against the action.
Mr Brown has declared simply that the decision to question Mr Green and search his home and offices was "a matter for the police" of which he had no prior knowledge.
But the Tory leader said the now PM had "made his career from passing on Whitehall leaks...and he'll be guilty of hypocrisy if he doesn't speak out".
Writing in the News of the World, he said: "When it comes to vigorous opposition, if this approach had been in place in the 1990s, then Gordon Brown would have spent most of his time under arrest."
"The Prime Minister has simply repeated that he 'had no prior knowledge' and this is 'a police matter'. Frankly, that's not good enough.
"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?"
Mr Cameron also turned his fire on the Commons authorities for apparently "not thinking twice" about allowing officers to raid his immigration spokesman's office in Parliament.
Speaker Michael Martin has faced calls for his resignation over the matter.
Mr Martin's office has said only that "there is a process to be followed and that was followed" but the Home Office confirmed permission would have been required from the House authorities.
Mr Green has expressed astonishment at being detained, insisting that he had been doing his public duty in holding the Government to account and would continue to do so.
Mr Cameron wrote: "Of course no one is above the law. But in a democracy there is an important line to be drawn when it comes to acting in the public interest."
Ms Smith said reports that Mr Green's conversations had been bugged as part of the operation were "conspiracy theory".
"If that were the case I would have signed a warrant. Home Secretaries don't confirm or deny which warrants they have or haven't signed.
"Frankly, let me be clear, we are getting totally into conspiracy theory territory, totally into conspiracy theory territory," she said.
Pushed several times to offer an apology to Mr Green and his family - who were at home at the time of the search - Ms Smith insisted she should not interfere.
"The idea that you charge into or impact on operational independence when things get a bit hot is not a principled position.
"I believe in the principle of the operational independence of policing and that's what I am carrying out."
The Metropolitan Police, who also face serious criticism of what Mr Cameron called "heavy handed" tactics, strongly denied a report in the Mail on Sunday that attempts were made to entrap Mr Green using phone calls from the official after he was arrested.
"We strongly refute any suggestion that an officer has acted improperly," a spokeswoman said.
Shadow home secretary Dominic Grieve said he believed Ms Smith "knew very well" that an MP was being drawn into the investigation, but had "just decided to sit back on her hands".
"She is the person who is ultimately accountable to Parliament for police failings," urging her to answer dozens of detailed questions over her role published by the Tories.
"If it turns out, which I think it may well do...that the police were barking up the wrong tree and pursuing an MP doing his legitimate job then I think she has a great deal to answer for."
He insisted there was "no evidence" that the civil servant concerned, who is reported to have sought a job with the party, had been offered any inducement to provide information.
"My understanding of the matter is that no-one has ever offered him a job or an inducement in order to do anything," he told Sky News Sunday Live.
"If there was a question of inducements being offered, that would produce a different situation. But the fact is there is no evidence of that."
He also questioned whether the police had misled the Commons authorities after it was reported that Serjeant at Arms Jill Pay said she had understood the operation had been cleared with senior law officers.
"One way of reading the contradictory explanations between the Serjeant at Arms and what the DPP (Director of Public Prosecutions) has said is that the police misled her.
"That is a very serious issue that needs to be looked into."
Mr Grieve said the Home Office "appears to have failed appallingly to control this process at all through accountability processes".
"All sense of proportion and common sense seems to have been lost. I don't think this would have happened in the past.
"Home Secretaries would not have intervened operationally but they would have said 'hang on a minute, are you sure you know where you are going, have you consulted with the law officers, are you really sure about the allegations?'
"All these checks, which I would expect to see work in a healthy democracy, seem to have been abandoned and I think we should be worried about that."
The police appeared to have been acting on "absolutely flimsy and trivial grounds", he suggested.
"That is a disaster for our country if that is allowed to continue."
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