The action on 4 October coincides with one of the dates chosen by the train drivers’ union, Aslef, for the next round of national rail strikes in a long and bitter dispute about pay and working arrangements.
On the Tube, the RMT says it has been “locked in a long-running dispute over 600 station staff cuts and detrimental working conditions since last year”.
Union leaders say they have safety concerns over “fewer staff facing higher workloads, more lone working and increased fatigue”.
The RMT general secretary, Mick Lynch, said: “Station staff have had enough of having their livelihoods threatened by job losses and attacks on their terms and conditions.
“These job cuts and attacks on conditions are going to lead to more unstaffed stations, temporary closures and rising passenger anger.
“This strike action will lead to the Tube being shut down and we call on Mayor Sadiq Khan to meet us urgently to discuss this matter.”
Previous strikes by RMT members on the London Underground have led to a near-total shutdown of the system.
Glynn Barton, chief operating officer for Transport for London, said: “We are disappointed that the RMT has announced strike action despite our open discussion on these issues.
“Nobody wants to see strikes that will cause significant disruption to our customers and we urge them to reconsider and continue engaging with us.”
On 4 October the Tube had been expected to carry more passengers than usual as commuters in the London suburbs and Home Counties switched from national rail to the Underground.
The second date of the strike, Friday 6 October, coincides with the final day of an overtime ban by members of Aslef. That action begins on Friday 29 September.
Together with another Aslef national walk-out on Saturday 30 September, rail passengers in the London area face a full week of disruption.