The RMT has suspended strikes due to be held on March 30 and April 1, the union has announced.
The move follows further discussions between the union and the Rail Delivery Group in the long-running dispute over pay, jobs and conditions.
The union has already resolved its row with Network Rail in a similar dispute.
“We are now jointly focused on working constructively towards a settlement to this dispute, which will mean we can do what we have always wanted to do – give our people a pay rise and help secure the long-term future of the railway with rewarding careers for all those who work on it.”
An RMT statement said: “Following further talks between RMT and the Rail Delivery Group today, a proposal was tabled by the RDG which could lead to a resolution to resolve the current national rail dispute through a new offer.
“The NEC has therefore suspended strike action scheduled for March 30 and April 1.
“RMT will have further talks with the RDG with a view to securing a new offer on pay, job security and working conditions.
“The dispute remains on and the union will continue to make preparations for a reballot when the current mandate runs out in mid-May.”
A Department for Transport spokesperson said: “This marks a positive step and takes us closer to resolving this dispute.
“After Network Rail employees overwhelmingly voted to accept a similar pay offer earlier this week, we’re once again asking the RMT executive to do the right thing and put this fair and reasonable offer to its members, giving them the pay rise they deserve and helping us end this dispute.”