Pay will rise by 4% from January 2023.
NR was also offering no compulsory redundancies for general grades and controllers until January 31 2025.
Staff and their families will also get a 75 percent discount on leisure travel and no unagreed changes to terms and conditions of employment will be made, the union said.
Tim Shoveller, Network Rail’s chief negotiator, said: “This response from the RMT to a significantly enhanced offer exposes their true priority – using the British public and Network Rail workers as pawns in a fight with the Government.
“What use is a referendum that means that strike disruption is inevitable? At best it’s the tactic the RMT played in October by calling the strikes off at the last minute and causing immense disruption to passengers and vital freight routes.
“They are playing fast and loose with people’s Christmas plans and the new strike dates announced deliberately target vital engineering work designed to improve the railway.
“A significantly improved offer is now on the table that gives Network Rail workers job security, a decent pay rise and some other substantial benefits for employees and their families.”
Transport Secretary Mark Harper said: “It’s incredibly disappointing that, despite a new and improved deal offering job security and a fair pay rise, the RMT is not only continuing with upcoming industrial action but has called more strikes over Christmas.
“It’s especially disappointing given the TSSA union has described this new and improved deal as the ‘best we can achieve through negotiation’ and called off strikes.
“The Government has played its part by facilitating a fair and decent offer but, by instructing its members to reject it, the RMT has failed to play its part and our rail network now faces more harmful disruption rather than helpful discussion.”