Mayor of London Boris Johnson believes the aborted strike on London Underground was broken by commuter power.
RMT say "the ball is in management's court" while London Underground claim "the ball is now firmly in the RMT leadership's court".
The fight broke out as the train approached Aldgate East station on Monday night, hours after the Tube strike began.
Transport union the RMT is gathering its members together in central London as part of its campaign to halt cuts to Tube services.
The plans outlined by Mayor Boris Johnson include cutting the number of station staff, closing ticket offices, and introducing driverless trains.
The RMT says the austerity measures will not only mean job losses, but impact on safety and services.
The event aims to inform trade union members as well as the public about the issues and to discuss the next campaigning steps.
A planned tube strike by power workers on London Underground has been called off. Union members were due to walk out over the Bank Holiday weekend in a row over pay and conditions which could of disrupted services.
– Keith Greenfield, Managing Director of Heathrow Express
We ran a regular service for our customers during the last RMT strike at the end of April, and we will do it again this time.
The RMT's misguided decision to strike again ignores the reality that Heathrow Express needs to save £6m of cost over the next five years in order to secure its future and jobs for its people.
Burying one's head in the sand does not alter the fact we need to implement changes to secure our future. We would of course prefer to do this with the agreement of the trade unions to ensure the best outcome for everyone, including RMT members.
According the the union, Unite, London Underground faces the prospect of a complete shut down this Bank Holiday weekend as workers, who control the power to run the trains, prepare to strike.
Unite regional officer Hugh Roberts said:
"There is a real possibility that the underground could close down over the bank holiday weekend. Unite is working very hard to achieve a fair settlement for our members - and to avoid the industrial action. The ball is very much in the management's court."
– Richard Jones, London Underground
Unite, TSSA and RMT have raised a number of issues with us around workplace and terms and conditions relating to staff in our power control team, all of which are either being addressed or we are happy to discuss.
We are disappointed that the unions have chosen to call strike action and we would urge all unions involved in this dispute to continue discussions to resolve this matter without the threat of industrial action.
- 40 technicians, mostly members of the Unite union, are based at the power control room in Blackfriars where they provide the power for the 270 station underground network
- Talks are being held today between the unions and London Unerground management to resolve the dispute before the strike starts Saturday, and ends at 8am on Tuesday
Rail and Tube workers will stage strikes over the Bank Holiday weekend in separate disputes over pay, jobs and conditions.
RMT members at Heathrow Express will walk out for 24 hours from 3am on Friday, and again from the same time on Bank Holiday Monday. Unite union power control staff on London Underground will also strike for three days from Saturday in a dispute over pay and conditions.
Five men have announced their intention to take over from Bob Crow as head of the Rail, Maritime and Transport union following the 52-year-old's sudden death.
Acting general secretary Mick Cash, closely involved in talks which prevented a 72-hour Tube strike, will stand as will London regional organiser John Leach.
The current assistant general secretary Steve Hedley, pictured holding an assault rifle on his Facebook page, is also among the candidates.
Other candidates include former union president Alex Gordon and Alan Pottage, the RMT's Edinburgh-based national organising co-ordinator.
Nominations for the job close in early July and the result will be announced in September.
Londoners expecting to face the chaos of a Tube strike this morning can breathe a sigh of relief.
A last-ditch effort to avert the planned three-day strike was successful, with the announcement being made just hours before the industrial action was scheduled to begin.
London Underground bosses said yesteraday they are pleased with the result of the talks, but say more work is needed to resolve the disputes over the future of the Tube.