"RMT is fully committed to achieving a negotiated settlement and will be available in London for discussions for the whole weekend and beyond in order to achieve a settlement."
A planned strike over this week's bank holiday was suspended after Network Rail tabled a fresh pay offer.
NR originally offered a four-year deal - £500 this year, followed by three years of increases in line with RPI inflation.
The new offer was for two years - a 1% rise this year and around 1.4% next year, with no compulsory redundancies for the duration of the agreement.
An Acas spokesman said: "Talks took place at the conciliation service Acas this afternoon to attempt to resolve the Network Rail dispute. These talks adjourned early evening and will reconvene tomorrow morning."
