Talks between Network Rail and RMT bosses are continuing into the evening as the two sides try to negotiate a deal to avert strikes that will bring Britain's railways to a halt.
However, the two sides met again yesterday with the hope of agreeing a new deal and talks continued today.
"Your negotiating team was invited to further discussions at Acas on the Network Rail dispute at short notice this afternoon," said RMT boss Mike Cash in a letter to members on Friday.
"Discussions have commenced and our full team will be in London on Saturday morning to take the negotiations forward. 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."
Those talks, facilitated by Acas, are continuing into the evening as they try to thrash out a deal before the strike action which is scheduled to begin next week.
An earlier strike over the bank holiday was averted to give the union time to consider a deal, although that was later turned down.
If a new deal can't be reached during the ongoing talks, two strikes will disrupt travellers - the first starting at 5pm on 4 June and the second starting just after midnight on 9 June until 5pm on 11 June.