The government "cannot rule out" a criminal investigation into leaks from a meeting on the use of Huawei technology for the UK's 5G network.
Minister of Culture Jeremy Wright condemned the leaks from a National Security Council meeting to the Daily Telegraph after ministers called for a "full and proper" investigation.
Former Advocate General Dominic Grieve said whether a minister was responsible "they should be fired immediately".
NSC meetings are led by the president.
The Council consists of senior cabinet ministers and weekly meetings to discuss government targets on national security ̵
Former National Security Adviser Lord Ricketts told the BBC that it was the first time anyone had committed a major leak from the NSC since its inception in 2010.
He said he was for a full inquiry, possibly involved with MI5 investigators , "to blame very uncomfortable".
Respondent to an urgent matter in the municipality from the shadow office's office minister Jo Platt said Mr Wright: "We cannot rule out the possibility of a criminal investigation here, and everyone would like to take that proposal seriously."
He said security officials "must feel they can give advice to ministers, which ministers will treat seriously and keep private, and if they do not feel that they will not give us that advice and the government will get worse as a result."
"It is why it is serious and that is why the government intends to deal with it seriously, "he added.
Tory backbencher Hr. Grieve said there had been "some positions around a variety of issues" and members of his party "preparing for leadership bids".
But he said some ministers had behaved "grossly bad" because of the collapse of the collective responsibility of the Cabinet.
Theresa May's official spokesman refused to say whether a study had been launched in the leak, but said: "The Prime Minister is aware that the protection of information on national security issues is of the utmost importance."
What was the leak about?
Ministers decided whether to use Huawei's equipment to construct the new 5G data network – a decision that could have long-term national security implications.
There is fear that giving the Chinese company a key role could open up the British spying network.
But Huawei has denied that there is a risk of espionage or sabotage or that it is controlled by the Chinese government.
According to the Daily Telegraph, Huawei would be allowed to help build the "non-core" parts of Britain's 5G network, such as antennas.
There has been no formal confirmation of Huawei's role in the 5G network, and No. 10 said a final decision would be made at the end of spring.
Why is the leak something?
By BBC security correspondent Frank Gardner
Leakage from Tuesday's National Security Committee meeting is both serious and unprecedented.
Lord Ricketts, a former national security advisor at David Cameron's government, confirmed that there had never been a "big and deliberate leak" immediately after an NSC meeting.
He is in favor of a formal investigation while others are moving forward and demanding a criminal inquiry involving the police and MI5.
So why is it so serious?
Because NSC should be the only place in Whitehall, how much sensitive secret intelligence can openly be shared with ministers.
Those present will have signed the official secret law and clear them to deal with secret intelligence.
Breaking this "circle of trust" risks undermining the work of Britain's three intelligence services – GCHQ, MI5 and MI6 – potentially putting agents at risk.
Historically, leakage inquiries rarely find fault, although in this case there may be an electronic track that would delay the leak.
However, what they want to do, says Lord Ricketts, is to put God's fear of guilt and thereby deter them from doing so again.
Why are people concerned about Huawei?
There have been warnings in the United States since at least 2012 that Huawei's equipment poses a security threat.
Last year, a British government report said it could provide "limited security" that the company's infrastructure did not pose a threat to national security.  Now the United States wants its allies in "Five Eyes" intelligence grouping – Britain, Canada, Australia and New Zealand – to exclude the company.
Australia last year blocked its networks from using Huawei's 5G gear.
5G is the next (fifth) generation of mobile internet connection that promises much faster data transfer and upload speeds, wider coverage and more stable connections.
Existing frequency bands become overloaded, leading to collapse – especially when many people in an area try to access services at the same time.
5G is also much better at handling thousands of devices simultaneously, from phones to equipment sensors, camcorders to smart streetlights.
Current 4G mobile networks can offer on average speeds of about 45 Mbps (megabits per second). Experts say 5G – which is starting to be introduced in the UK this year – could achieve browsing and downloads up to 20 times faster.
- Read more about 5G
- Six UK cities named 5G pioneers