The RMT has suspended plans for rail strikes on 30 March and 1 April.
The union had scheduled the walk-outs as part of a long-running dispute over pay, jobs and conditions for staff working across 14 rail operators.
It comes after the RMT announced on Monday that union members at Network Rail had voted to accept a revised pay offer in a similar dispute.
In a statement, the union said: "Following further talks between RMT and the Rail Delivery Group [RDG] 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 National Executive Committee has therefore suspended strike action scheduled for 30 March and 1 April."
The union said it would hold 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 re-ballot when the current mandate runs out in mid-May," the union added.
The latest suspension moves the country closer to an end to the long-running dispute between the rail unions and train operators, with no more nationwide strikes by the RMT currently in the pipeline.
The union says it maintains smaller local disputes. The train drivers' union ASLEF has yet to settle its dispute, however, no more strikes are currently scheduled.
Members of the TSSA union accepted an offer in February, while Unite members working in Network Rail control rooms also accepted a deal in December.
A Rail Delivery Group spokesperson welcomed the RMT's move to suspend the strikes.
"This is great news for our customers and for our staff," the spokesperson said.
"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."
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."