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”.
Meanwhile, Tory leadership rival Boris Johnson has insisted only he can beat both Nigel Farage and Jeremy Corbyn.
And Home Secretary Sajid Javid, another of the 11 Tory MPs who have said they want to replace Theresa May, received a boost to his leadership campaign on Saturday after he was backed by Scottish Conservative leader Ruth Davidson.
Mr Gove announced his plan to replace VAT in the Sunday Telegraph, writing that his “business know-how” had allowed him to bring in positive changes to education, the environment and the justice system while in his various ministerial roles.
“My economic plan is driven by the need to increase investment, productivity and wages across the country, with a special focus on helping those areas and regions where productivity is lower,” he wrote.
“It would mean reducing the regulations which hold business back, cutting and reforming taxes – such as business rates – which put pressure on small businesses and undermine our high streets, using the opportunity of life outside the EU to look to replace VAT with a lower, simpler, sales tax,” he added.
Mr Gove, who is due to appear on the BBC’s Andrew Marr Show later, admitted on Friday to taking cocaine at several “social events” more than 20 years ago.
Speaking on Sunday, Mr Javid said it was not for him to “pass judgment” on fellow leadership contenders, but stressed that people who take class A drugs should think about the entire supply chain.
“Anyone who takes drugs should be thinking about how they are not just hurting themselves, but about how they are destroying so many countless lives along the way”, he told Sky’s Sophy Ridge on Sunday programme.
Fellow leadership hopeful Dominic Raab, who has previously admitted smoking cannabis, told the BBC’s Today programme the admission should not result in Mr Gove being barred from the race.
Some of the other candidates have also admitted taking drugs – including Rory Stewart, who has apologised for smoking opium at a wedding in Iran 15 years ago, and Jeremy Hunt, who told the Times he had drunk a cannabis lassi while backpacking through India.
And in an appearance on Have I Got News For You in 2005, Mr Johnson admitted being given cocaine 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.”
However, the emergence of Mr Gove’s 1999 article has led to criticism in the Mail on Sunday and the Observer who quote criticism from drug charities and former police officers.