The move comes after the union received a revised pay proposal from management at Rail for London Infrastructure (RfLI) and will now consult members about the way forward.
In January, the dispute saw a one-day stoppage by dozens of TSSA members working on the rail line after it emerged some Elizabeth Line staff were paid thousands of pounds less than colleagues performing similar roles on other parts of the Transport for London (TfL) network.
TSSA interim organising director, Mel Taylor, said: "We have had a very constructive meeting and as a result TSSA has agreed to suspend the strike action planned on 24 May.
"This will enable our teams to fully digest the changes and allow for further consultation and discussion over the coming days.
"We certainly do not take strike action lightly, but we have made this progress as a result of the action we have taken and planned to take."
