Speaking at Mayor’s Question Time, Boris Johnson said: "There has been an increase in reporting of cybercrime and it is a very, very important issue."
"Firms across London are anxious about it, as it is a crime type that is going up," he added.
When asked if he agreed with proposals that London firms should sign up to a voluntary minimum standard of cyber-security, he added: "It sounds like a very interesting idea that this place [City Hall] should be taking forward."
"I don't know whether I've got much time to develop it myself, but it's a very good idea," Johnson said.
The mayor also said it sounded like a "good idea" to publish company names that had signed up to the standards, so customers knew who to trust their data with.
Johnson's comments come after Evans said the mayor should back calls to make it compulsory for companies to declare when they have suffered a cyberattack.
This would include the minimum standard would better inform consumers about which companies in London are taking cyber security seriously.
Evans has said that this standard would incentivise businesses in London to maintain a high level of cyber-security.