The union confirmed to AAP on Friday the planned action, driven by safety concerns over a new fleet of Korean-built trains, will start Tuesday and continue throughout the week.
Finance Minister Damien Tudehope and Transport Minister David Elliott attended the 5pm Friday meeting, after one scheduled for the morning was cancelled.
Train drivers will drive slower and refuse to operate foreign-built trains as part of four days of industrial action, which was announced after the cancellation of the 9am Friday meeting.
The union's secretary Alex Claassens said he was told the morning meeting had been cancelled about 10pm on Thursday while taking part in the Vinnies CEO Sleepout, with no explanation given.
Transport for NSW notified the union on Friday afternoon of a meeting at 5pm, giving the government one last chance to halt industrial action scheduled to begin Tuesday.
Mr Claassens said the government must agree to alterations to the new intercity fleet trains, the first of which was delivered in 2019 but has never gone into service.
Treasurer Matt Kean said in May it was costing the government about $30 million a month to store the trains.
Mr Claassens said he had been tipped off prior to the budget that a $300 million line item would fix issues the union claims make the train unsafe, but has since learned the money is part of the existing contract.
Mr Tudehope was asked at a press conference on Thursday if the money in the budget was for the union's requested alterations.
"I'll take that on notice," he told reporters.
"There are still negotiations to take place in relation to how we reach an agreement with the union in respect of the variety of claims that they are making."
Mr Tudehope said the new trains are state of the art and have been approved by the Office of the National Rail Safety Regulator.
The industrial action will begin on Tuesday with a go-slow movement when drivers will not exceed 60 km/h.
On Wednesday, members are indefinitely banned from moving back to the rail operations centre, and would only work from their current depot on Thursday, while there will also be an indefinite ban on work relating to Sydney Metro.
On Friday members would refuse to drive foreign-built trains, taking new trains introduced since 2011 out of service.
Mr Claassens said the network would run at about 30 per cent capacity without those trains, which it has done in recent months when the union took similar action.
"Management's got a timetable that they can run where they know the trains that they can use and how that will operate," he said.
"They've done it before, they can do it again."
Mr Claassens said workers have been acting in good faith during the long-running negotiations for a new enterprise bargaining agreement after the old one expired more than a year ago, but their patience is wearing thin.
"To be honest they're a little bit frustrated with me and other people who were saying to them, 'Let's give the government the opportunity to come good on this' ... They've had plenty of time and yet they keep stalling," Mr Claassens said.
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