Michael Gove has admitted he was "fortunate" to avoid prison after using cocaine several times 20 years ago.
The Tory leadership hopeful previously said he took the class A drug while working as a journalist.
Asked if he should have gone to prison, Mr Gove told the Andrew Marr Show: "I was fortunate in that I didn't, but I do think it was a profound mistake."
Tory leadership rival Sajid Javid said people who took Class A drugs needed to understand the damage they were doing.
Speaking to Sky's Sophy Ridge on Sunday, home secretary Mr Javid said: "It doesn't matter if you are middle class or not - anyone who takes class A drugs, they need to think about that supply chain that comes from Colombia, let's say, to Chelsea and the number of lives that are destroyed along the way."
'It was a crime'
Apologising for taking cocaine, Mr Gove said: "I deeply regret the mistake that I made.
"It was a crime, it was a mistake."
However, the environment secretary denied he had ever had a drug "habit".
A Times article Mr Gove wrote in 1999 - around the time he admits having taken the drug - has been republished.
In it he criticised "middle class professionals" who took drugs - leading to headlines calling him a "hypocrite".
But speaking on Marr on Sunday morning, Mr Gove denied that amounted to hypocrisy.
"I think anyone can read the article and make their own minds up," he said. "The point that I made in the article is that if any of us lapse sometimes from standards that we uphold, that is human.
"The thing to do is not necessarily then to say that the standards should be lowered. It should be to reflect on the lapse and to seek to do better in the future."
'No one asked'
When asked if he had declared his drug use on his Esta form for entry into the US, under the visa waiver scheme, he replied: "I don't believe that I have ever, on any occasion, failed to tell the truth about this when asked directly."
He added: "I think it is the case that if I were elected as the prime minister of this country then of course it would be the case that I would be able to go to the United States."
And asked if he had declared his drug use before becoming a minister, Mr Gove replied: "No one asked. The question was never raised."
Mr Gove, who served as justice secretary from 2015-16, is one of 11 Tory MPs who have said they intend to stand in the contest to replace Theresa May, with the winner expected to be announced in late July.
International Development Secretary Rory Stewart, who is one of those standing against him, has already apologised for smoking opium - a class A drug in the UK - at a wedding in Iran 15 years ago.
Boris Johnson, the favourite to succeed Mrs May as Conservative leader, was asked about claims he had taken cocaine at university by Marie Claire magazine in 2008.
He replied: "That was when I was 19."
In an appearance on Have I Got News For You in 2005, he admitted being given the drug but suggested he had not actually taken it, saying: "I think I was once given cocaine but I sneezed and so it did not go up my nose. In fact, I may have been doing icing sugar."
Andrea Leadsom told the Independent that she "smoked weed at university" but had "never smoked it again since".
On Saturday, Dominic Raab, who has previously admitted smoking cannabis, told BBC Radio 4's Today programme: "I think Michael has set out that he made a mistake.
"It was a long time ago, people will judge it as it is but I do believe in a second chance society."
And Foreign Secretary Jeremy Hunt - another candidate - told the Times he had drunk a cannabis lassi while backpacking through India.
'All the tools at our disposal'
Esther McVey, who is also hoping to become the new Conservative Party leader, told the Marr show she had never taken class A drugs.
She later told ITV News that she had tried cannabis when she was "much younger".
Ms McVey also accused MPs trying to prevent Brexit of "tearing up 400 years of history", as she defended her right to prorogue Parliament - essentially shutting it down - to leave the EU without a deal if she became prime minister.
The former work and pensions secretary said it would not be her "priority" to suspend sittings in the House of Commons in the run-up to the 31 October deadline - but said she would be willing to "use all the tools at our disposal" if she won the race to replace Mrs May.
Mr Gove said such a move would be "wrong" and contradict "the best traditions of British democracy".
Mr Hunt, meanwhile, said Angela Merkel told him the European Union "would be willing to negotiate" on the Brexit deal with a new prime minister.
The foreign secretary claimed the German chancellor said Brussels "would look at any solutions" the UK puts forward to solve the Northern Irish border issue as he tried to emphasise his credentials as a deal-maker in the race to replace Mrs May.
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