Members of Aslef were due to stage a series of walkouts which would have caused travel disruption in the capital.
Aslef said its executive will consider a revised offer from the line’s operators MTR, tomorrow.
Strikes planned for Thursday and Saturday have been suspended but no announcement has been made about further strikes next month.
Howard Smith, Transport for London’s director of the Elizabeth line, said: “We are pleased that Aslef has suspended its first two dates of planned industrial action on the Elizabeth line after a revised offer has been made.
“This is good news for Londoners, and we encourage Aslef and MTR Elizabeth line to continue working constructively to avoid any future disruption and address concerns.”
