Members of the British Airline Pilots Association (Balpa) said talks had been held to try to resolve the row.
The union said proposals to mitigate pilot fatigue would now be put to members in a ballot.
Brian Strutton, Balpa's general secretary, said it did not mean the dispute was over, but "sufficient progress" had been made.
He said: "We have been working hard today and over the last few days to find a solution to this dispute about pilot fatigue.
"Easyjet management have put a proposal on the table that the Balpa team feel has closed the gap between us considerably on a range of issues.
"We therefore feel it is right and proper to consult with our members at this stage and so we are suspending serving notice of industrial action on the company."
It was revealed earlier this month that pilots were considering strike action over the week that coincides with the half-term holiday in many schools.
In a letter to pilots leaked to The Daily Telegraph, Balpa outlined strike action blaming a "dispute with Easyjet purely concerning pilot fatigue".
It claimed the core issue of the dispute was that "fatigue had risen year on year, to levels pilots and Balpa find unacceptable".
The airline said the new proposal had been developed after "extensive" discussions and would be put to its UK pilots in the hope that a "mutually agreeable solution" could be reached.
This meant there was currently "no threat of strike action", it added.
Easyjet pilots have suspended their plans to strike, while new proposals on tackling fatigue are considered.