Bob Crow has called in to Boris Johnson's LBC 97.3 phone-in saying: "All we want is to express our view. All we want is in an opportunity to talk."
Boris Johnson responds by saying: "The best way to engage is to call off the strike and I will be happy to sit down and talk... but I can't sit down and negotiate with a gun held to the head of Londoners."
The confrontation came during the Mayor's monthly phone-in show on LBC 97.3 - thought to be only the second time the two men have spoken.
The dispute over ticket office closures was deadlocked tonight with millions of commuters almost certain to be caught in the crossfire.
London Underground says services will be affected from around 9:30pm on Tuesday 4 February.