There were no talks scheduled to take place today between the RMT, Unite – which is also calling members out on strike - and Transport for London, though TfL said it remained willing to talk and keen for the action to be called off.
Union sources said talks were held at Acas last week but no progress was made.
Mr Khan said the strikes – which have been called in response to the axing of up to 600 station posts and feared changes to the TfL pension scheme – were the result of the Government “micro-managing” TfL.
Claiming that “strikes ultimately resolve nothing”, Mr Khan said: “I say to the RMT: we haven’t changed any pension conditions, no jobs have been lost, but you are punishing the wrong people by going on strike on Tuesday - the businesses that struggle, those who need to get to their place of work but can’t do so, who have appointments and so forth. Their grievance is with the Government not London or TfL.”
Tuesday’s action follows 24-hour strikes by the RMT on March 1 and 3 and on June 6.
TfL expects “severe disruption or no service” across the Tube, with services not restarting until 8am on Wednesday and taking until lunchtime to return to normal.
However the Elizabeth line will run a reduced service between Paddington and Abbey Wood from 7am to 6pm on Tuesday, and some services on the line east of Liverpool Street and west of Paddington until around 4pm.
There will also be some trains on the London Overground between 7.30am and 6pm, but services are expected to be very busy and may not call at all stations.
DLR stations that also serve London Underground may be closed.
Picket lines are expected outside more than 50 Tube stations or depots, including Victoria, Brixton, Leicester Square and Oxford Circus.
Andy Lord, TfL’s chief operating officer, said: “I want to apologise to TfL’s customers for the impact these strikes will have on their journeys and urge people to avoid travel on all TfL services on June 21 unless absolutely necessary.
“The strike on the London Underground has been timed by the RMT and Unite unions to cause maximum disruption to our millions of customers by coinciding with strike action on national rail services.
“Additional strikes on national rail services next week will also have an impact on London Underground, Overground and Elizabeth line services because of shared track and assets.
"This strike is particularly frustrating as it comes so soon after industrial action earlier this month, no changes have been proposed to pensions and nobody has or will lose their job as a result of the proposals we have set out.
“We’re urging the RMT and Unite to call off this strike – my message to them is that it’s not too late to work with us to find a resolution and avoid the huge disruption this action will cause."
The two Tube strikes in March, which shut more than 200 stations and reduced passenger numbers to four per cent of normal, cost TfL an estimated £13m in lost fares.
More than 15,000 Tube staff began receiving an 8.4 per cent pay rise from April.
TfL on Monday insisted it had met every one of the 60 conditions attached by the Government to its four covid bail-outs, including the requirements to make massive savings.
TfL’s current deal runs out on Friday. TfL is seeking £900m for the remainder of the 2022/23 financial year plus a long-term capital funding settlement.
TfL said it generated £616m in fares income in April and May - almost £250m more than last year but about £120m lower than pre-pandemic levels.
However its income from road charges such as the congestion charge and Ulez has fallen – with fewer motorists paying the levies, and more seeking to delay or avoid the penalty charges.
TfL said: “This is likely being driven by cost of living challenges and increasing fuel prices.”
A DfT spokesperson said: "The Government has clearly said it does not want these strikes to go ahead. We urge unions to engage in meaningful talks with the rail industry and work together towards a more modern, passenger-focussed railway. It is not for the Government to attend such talks as we are not the employer."