Union leaders at the RMT have accused the contractor of “bully-boy” tactics during talks and of withdrawing a previous pay offer.
Union members are now planning not to book in for shifts on Saturday and Sunday.
But Amey hopes to head-off the action with further talks planned for today.
A company statement said: “We aim to be an equitable employer and our focus is on achieving the long-term aims of the rail industry along with fair pay for our employees.
“Amey remains in negotiations with the RMT. As part of the negotiation process, we put forward an extremely competitive pay offer, which would be withdrawn if the RMT progressed strike action. Unfortunately, the RMT did progress strike action.
“Amey and the RMT are due to have further talks today and hope to reach a swift resolution.”
RMT General Secretary Bob Crow said: “Amey are a highly profitable and high profile company working on a range of key rail projects, including electrification, and yet here they are treating the staff that they rely on to deliver their contracts and generate their profits like dirt.
“Pulling the current offer, instead of getting round the table and negotiating a way forward in this dispute, is a confrontational and provocative act.
“In view of Amey’s complete intransigence throughout negotiations, and their decision to resort to pure bully-boy tactics, our representatives and members feel that there is no alternative to taking further industrial action and we are in no doubt that our members will remain rock-solid in this dispute and determined to win a fair deal.
“RMT remains available for talks and the ball is now firmly in Amey’s court.”