BBC political correspondent Nick Eardley said, as a frontrunner for the leadership contest, Mr Gove's confession was more significant than Mr Stewart's.
And Foreign Minister Jeremy Hunt, 52, said he might have drunk a milkshake that was laced with drugs when he was younger.
Mr Gove said: "I hugely respect Cressida Dick and one of the things I would absolutely say is that it is a mistake I profoundly regret, absolutely".
An upcoming biography of Gove includes the revelation of his drug use.
"Obviously it will be for my colleagues in parliament and members of the Conservatives Party to decide now if I should be leader", he added.
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"I believe that every life is precious and that everyone has worth and that whatever people have done in the past, we should look for the treasure in the heart of every man and try to give people the change to make a contribution". International Development Secretary Rory Stewart told the Telegraph he smoked opium at a wedding in Iran 15 years ago.
Johnson, who was married to Indian-origin Marina Wheeler and is the favourite to win the election and enter 10, Downing Street, has previously admitted to taking cocaine while at the University of Oxford: "That was when I was 19". At the time I was a young journalist. "Certainly when I was working as a journalist I didn't imagine I would go into politics or public service.The question now is that people should look at my record as a politician and ask themselves, 'Is this person we see ready to lead now?'" He says he won't criticize anyone for "holding their hand up and saying 'I got that wrong'".
Leadership nominations will close at 17:00 BST on Monday, the party has said.
His admission to taking the drug could put him in breach of visa rules, which require the applicant to answer whether they have ever violated laws related to possessing, using or distributing illegal drugs.
"I have seen the damage drugs can do to others and that is why I deeply regret the decisions I took", he added.
Health Secretary Matt Hancock is understood to have tried cannabis as a student but has not used drugs since university.