The Mayor of London has the power to make coverings mandatory on the TfL network but said he decided not to do so before it became government policy to ensure "message clarity".
Transport Secretary Grant Shapps hit back at Mr Khan's allegations saying he was “disagreeing with the scientists”.
Face coverings are due to become mandatory on all forms of public transport in England from mid-June.
Mr Khan told BBC Breakfast he had been lobbying the government to make coverings mandatory on public transport for two months.
He added: “The evidence was quite clear in late March early April when I was speaking to colleagues around the world who were doing this.
“My concern about going it alone was it is really important when you’ve got a crisis that we have message clarity and that we have a national consensus.
“For example, in London not all the public transport is under my control and what we didn’t want was confusion in relation to those commuters coming in from outside London to London.
“But also a blurring of the messaging. So that’s why it was important to try and persuade the government to do the right thing.
“My concern – and I’ll go as far to say my anger – is the delay it has taken because this could mean more people having caught the virus in the community because there are some times you simply can’t keep your social distance and this delay I think has been good for nobody.”
Pressed on why he did not bring in coverings sooner in London, the Mayor replied: “There are big concerns in relation to London having a different message to the rest of the country.
“The government has been keen on – and I support them on this – on having a national response to both going in to lockdown and easing lockdown.”
Mr Shapps was asked about the Mayor’s comment that the delay was “good for nobody” and alluding that it could have prevented more deaths.
The Secretary of State replied: “Well he is disagreeing with the scientists if he’s saying that because the scientists have been very clear that they have been struggling to provide the conclusive evidence on it.
“On balance we are convinced it certainly can’t do any harm. We think it will do some good.”
Earlier in the interview, Mr Shapps was quizzed on why they did not bring the rule in earlier and he replied: “The evidence looks quite marginal on this. There is quite a lot of argument and debate amongst the scientists on it.
“But the reason now, or rather Monday week on the 15th, is that’s actually when we will see a big uplift in terms of the number of people using public transport.
“Because that’s when non-essential retail returns and when some secondary schools, I think years 10 and 12 come back, so we expect to see more people on the transport system.”
Commuters could be fined or refused permission to board buses or trains if they do not comply with the order aimed at stopping the spread of coronavirus.