Gavin Williamson has strenuously denied he leaked information from the National Security Council as calls are being made for a police inquiry.
He was sacked as defence secretary for allegedly disclosing plans to allow Chinese telecoms giant Huawei to help build the UK's 5G network.
Opposition MPs said there should be an investigation into whether the Official Secrets Act had been breached.
Downing Street said it had "compelling evidence" and the matter was closed.
Mr Williamson is quoted in several of Thursday's newspapers as saying he was the victim of a "vendetta" and a "kangaroo court".
He told Sky News that he "swore on his children's lives" that he was not responsible for the leak.
He also cited poor relations with Sir Mark Sedwill, the Cabinet Secretary and National Security Adviser, who carried out the leak investigation, telling the Times he would have had been "absolutely exonerated" had police probed what went on after the NSC meeting.
The inquiry into the leak began after the Daily Telegraph reported on the council's confidential discussions - including warnings from several cabinet members about possible risks to national security over a deal with Huawei.
At a meeting with Mr Williamson on Wednesday evening, Theresa May told him she had information that suggested that he was responsible for the unauthorised disclosure.
In a letter confirming his dismissal, she said: "No other credible version of events to explain this leak has been identified."
In response, Mr Williamson - defence secretary since 2017 - wrote he was "confident" that a "thorough and formal inquiry" would have "vindicated" his position.
"I appreciate you offering me the option to resign, but to resign would have been to accept that I, my civil servants, my military advisers or my staff were responsible: this was not the case," he said.
BBC political editor Laura Kuenssberg said sources close to the former defence secretary had told her Mr Williamson did meet the Daily Telegraph's deputy political editor, Steven Swinford, but "that absolutely does not prove" he leaked the story to him.
Labour deputy leader Tom Watson told BBC Radio 4's Today programme that Mr Williamson has "a right to clear his name" and the best way to do that is through a criminal inquiry.
He said: "This is about the law applying equally to everyone. We have had very high profile civil servants going to jail for breaching the Official Secrets Act."
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