"I don't believe that past mistakes should disqualify you", Gove said.
On Mr Gove's admission, Mr Javid - who is also standing to succeed Theresa May as prime minister - told Sky News' Sophy Ridge on Sunday programme: "Anyone that takes Class A drugs, they need to think about that supply chain that comes from Colombia to, let's say, Chelsea, and the number of lives that are destroyed along the way". Conservative lawmaker Rory Stewart joined the fray at the end of May, confessing to smoking opium at a wedding in Iran.
Foreign Secretary Jeremy Hunt told the Times he thought he tried a cannabis lassi whilst backpacking through India, adding it was "almost as naughty as wheatfields".
Mr Gove was never asked the question during the campaign but was eliminated in the second round.
Meanwhile, in what appears to be a current freaky trend of attempting to appear more street-wise and "down-to-earth" to Tory members (i.e. voters in the impending leadership race), Rory Stewart, another of the Tory leadership contenders, recently apologised after admitting he had smoked opium at a wedding in Iran.
Gove, a former journalist, admitted to the Daily Mail on Saturday: "I took drugs on several occasions at social events more than 20 years ago". It was a mistake. "I look back and I think I wish I hadn't done that", he said. Certainly when I was working as a journalist I didn't imagine I would go into politics or public service.
Mr Gove admitted he was "fortunate" not to go to jail, adding: "I do have a profound sense of regret about it all and I am very, very aware of the damage that drugs do".
Mr Gove insisted he had committed a mistake "I profoundly regret", and insisted he is "committed to helping everyone" moving away from drugs.
Theresa May stepped down on Friday as leader of the Conservative Party, but will remain as prime minister until her successor is elected and takes over from her in July, after completion of the two-phase leadership election.
Nominations for the Tory leadership contest close on Monday.
The first phase will see party MPs vote in several rounds from next week until the candidates are whittled down to two.