But Robert Jenrick insisted it would not be "sensible or reasonable" to hand over ministers' documents or messages deemed irrelevant to the pandemic as the Government takes the official investigation to court.
It comes after the former prime minister was warned he could lose public funding for legal advice if he tries to "frustrate or undermine" the Government's position.
Cabinet Office lawyers wrote to Mr Johnson, warning that money would "cease to be available" if he breaks conditions such as releasing evidence without permission.
Mr Johnson has been at the centre of a row as ministers launched a High Court bid to challenge the inquiry's demand for his unredacted WhatsApp messages and notebooks.
He vowed to send all his messages to the official investigation directly, circumventing the Cabinet Office.
Advice
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