Talks between Sydney Trains bosses and union officials over pay and conditions remain deadlocked despite a marathon 10-hour meeting on Monday.
Talks will resume on Tuesday afternoon.
Ms Berejilkian urged all parties to put aside their differences and do what's in the best interest of customers.
She said the state will do everything it can to prevent more than 9000 train workers stopping work next Monday.
"We do have legal recourse and we will be taking that action but of course our preference is that negotiations end in a positive way and that the strike action be averted," she told reporters in Sydney on Tuesday.
The union is pushing for a six per cent pay rise and improved conditions, while the government upped its offer to 3 per cent overnight after previously holding firm on a 2.5 per cent increase.
Rail, Tram and Bus Union NSW secretary Alex Claassens says it's not just about money.
The main issues revolve around resourcing, rostering and job security.
He is frustrated that Transport Minister Andrew Constance - who hasn't been in the meetings - is focusing on pay over conditions.
"It's not going to help the negotiations. In fact, it will probably derail it," Mr Claassens told 2GB radio on Tuesday.
Unless management addresses the union's concerns about conditions the proposed ban on overtime work will start on Thursday followed by the strike on Monday, he said.
"We're just frustrated."
Mr Constance insists the government made an offer good enough to stave off the strike.
"We have put the offer to them and it is up to them to hopefully get this good package in place," he told the Seven Network on Tuesday morning.
Passengers endured a horror week on the rail network earlier in January, with delays and cancellations leaving thousands stranded during peak hour. More than a dozen commuters and staff were injured on Monday after a train slammed into a barrier at Richmond Station, in Sydney's northwest.
The Australian Transport Safety Bureau, Office of Transport Safety and the Office of National Rail Safety Regulator are investigating the incident.
