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.
The planned three-day strike by London Underground workers has been suspended, the RMT Union has said.
The London Underground and Rail, Maritime and Transport are holding last-ditch talks just hours before a three day strike, that could affect millions of people across London and surrounding areas.
Conciliation service Acas said the talks between the RMT and London Underground started at 10am.
RMT union members are set to walk out of their jobs for three days at 9pm this evening, in a long-running dispute with the London Underground over ticket office closures.
A two-day strike last week caused huge disruption, with roads clogged as people switched to other forms of transport.
London Mayor Boris Johnson claimed this evening that London is being 'held to ransom' by the RMT Union over next week's planned Tube strike.
His comments came as talks between London Underground and unions bosses finished today with the planned three day stoppage still on.
The Mayor said: said: "Once again London is being held to ransom by a minority of just one union, the RMT, who, unlike the other three unions, and on a ballot taken last November with just 30 per cent support, is digging in its heels and refusing to play its part in shaping the future of the Tube."
"Less than three per cent of journeys involve a visit to Victorian era ticket offices, which cost Londoners £50 million a year to run. It makes absolutely no sense to keep them open.
RMT said after "eight hours of talking about very little" next week's 72-hour Tube strike was still on.
"They have spent eight hours talking about very little so regrettably the strike is still on," the RMT's John Leach said outside Acas.
Next week's planned 72-hour Tube strike is still on after talks between London Underground management and the RMT union broke down.
Boris Johnson has claimed that an RMT member told him not to "give in" on the issue of ticket office closures on the London Underground.
London Underground management and RMT leaders are involved in talks at conciliation service Acas as they attempt to avert a planned 72-hour Tube strike next week.
"He said 'I'm an RMT member. Whatever you do don't give in.This is the right thing to do' - and that's what we're going to do," the mayor said.
The union staged a 48-hour strike earlier this week.
Sandwiches have been served at Acas as talks between London Underground management and the RMT union continue.
ITV London's Political Correspondent Simon Harris tweeted:
The two sides in the tube dispute are still talking at ACAS. Sandwiches now being served. @itvlondon
Talks aimed at averting another round of strikes by London Underground workers will involve all four tube unions: RMT, Aslef, TSSA and Unite.
London Underground Chief Operating Officer Phil Hufton says three unions took part in a Piccadilly Line station-by-station review yesterday but the RMT boycotted.
The conciliation service Acas has confirmed it will host new talks between the Rail, Martime and Transport union and Transport for London in an attempt to resolve the London Underground dispute.
Members of the RMT union are preparing to strike for a further three days from 9pm on Monday 5th May if a resolution cannot be found.