The Berejiklian government has rejected calls for Sydney train passengers to receive fare refunds despite two days of chaos on the city's rail network.

While apologising to commuters for a "perfect storm" of events that led to major cancellations and delays, NSW Transport Minister Andrew Constance ruled out refunds because he said revenue from fares was needed to pay staff and run services.

"It was a perfect storm the last two days – we are not hiding from the fact that it was a mess. We want to apologise for that," he said. "The trick to this now is getting this back on track as quickly as we can."

Services across the rail network improved significantly on Wednesday, compared with the previous two days.