London Underground (LU) and an industrial union are at loggerheads over six planned Tube strikes.
LU has claimed the strikes planned to take place between 16 May and 17 June have been called off.
But the Rail Maritime and Transport union (RMT) insisted it has "not called off" the strike.
The RMT said it expected 1,500 drivers to walk-out in a row over the sacking of two drivers. LU had denied the union's claims of unfair dismissal.
The row revolves around Bakerloo Line driver Eamonn Lynch - who won his claim of unfair dismissal in an employment tribunal - and Northern Line driver Arwyn Thomas, who was also planning to take his case to an employment tribunal.
LU said following the tribunal's ruling Mr Lynch had been re-employed.
Mike Brown, LU's managing director, said: "Following a meeting with the RMT leadership this morning, the RMT have withdrawn their threat of industrial action, and we have avoided significant disruption for London.
"Responding to the results of the employment tribunal, not to the threat of strike action, London Underground has agreed to re-engage Mr Lynch in our employment in an alternative position and to discuss Mr Thomas' case further ahead of the planned tribunal."
But an RMT spokesman said the strike had not been called off.
He added: "The strike action in the victimisation dispute on London Underground has not been called off.
"We have not received confirmation of any potential offer from London Underground as a consequence of earlier talks.
"If and when any written confirmation of any offer is received it will be considered by our executive and a statement will be issued by the RMT."
Following LU's announcement London Mayor Boris Johnson said he welcomed the resolution as it showed the union has recognised "that flexing union muscle is completely unjustified and unnecessary".
"I am also pleased that the union has recognised that there was a significant safety breach in the case of Eamonn Lynch and that I, as mayor, will not tolerate the lives of Londoners being put at risk.
"The capital is rightly fed-up with pointless, futile and destructive strikes."