Members of the Rail, Maritime and Transport (RMT) union at Network Rail are due to walk out for 24 hours from next Thursday evening and 48 hours the following week, threatening travel chaos after a new pay offer was rejected.
A Network Rail spokesman said the company and the RMT have agreed to meet at the conciliation service Acas later today to try to resolve the dispute and avert strike action.
The RMT is planning the 48-hour strike from 5pm on June 9.
The workers, including signallers and maintenance staff, will also ban overtime from June 6-12.
A planned strike over the bank holiday was suspended after Network Rail (NR) 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.