Members of the Rail, Maritime and Transport union (RMT) had been due to stage 24-hour walkouts on Saturday and on Monday and Wednesday.
The RMT said it has secured “unconditional” talks on Network Rail (NR) and the promise of a pay offer from the train operating companies.
The union said the dispute remains “very much live” and it is continuing its re-ballot of members to secure a fresh mandate for action with the result due on November 15.
However, separate strikes planned by RMT for ScotRail services on November 19 and every Friday and Saturday in December until Christmas remain on the table.
Talks were held on Friday in a bid to break the deadlock, with Phil Campbell, ScotRail head of customer operations, describing the meeting as “constructive”. He said talks would continue next week.
RMT general secretary Mick Lynch said of the national strike suspension: “The threat of strike action and our strongly supported industrial campaign has made the rail employers see sense.
“We have always wanted to secure a negotiated settlement and that is what we will continue to push for in this next phase of intensive talks.
“Our priority is our members, and we are working towards securing a deal on job security, a decent pay rise and good working conditions.
“Our re-ballot remains live and if we have to take strike action during the next six months to secure a deal, we will.”
Tim Shoveller, Network Rail’s chief negotiator, said: “It’s welcome news that the RMT has called off its strikes, but the very late notice means that services for tomorrow cannot be reinstated and will remain extremely limited, and while we, and our train company partners, will work without pause over the weekend, there will be limited ability to change the ‘strike timetable’ for Monday.
“Our advice remains to please check before you travel and on Saturday and Monday and only travel by rail if absolutely necessary.
“We look forward to getting back round the table with all our trades unions early next week to see if the progress made this week can be built on, and a resolution found.”
A spokesperson for the Rail Delivery Group said: “It is positive that the RMT leadership have stepped back from the brink and called off their strike action.
“Unfortunately, the late notice means that while train companies are working hard to reinstate services, they will remain severely disrupted for our passengers tomorrow and into the early part of next week.
“Our advice remains to please check before you travel and on Saturday and Monday only travel by rail if necessary.
“We remain committed to intensive negotiations to agree the reforms needed to improve reliability, deliver a pay rise for our people and get the industry back on a sustainable financial footing.”
The RMT said NR had originally declared discussions and consultations closed and was intent on imposing changes to maintenance without agreement with the union.
“They have now rowed back and will continue discussions on the basis that “nothing is agreed until everything is agreed”.
“This takes away the reason for the current phase of action and means talks can continue without pre-conditions unilaterally set down by the company,” said the RMT.