It means bus services will operate as normal on 27-30 June.
The union will put the pay offer, which includes an increased hourly rate for senior drivers, to staff on Friday 27 June through a ballot.
The rate of progression between the different levels of pay has also been enhanced.
Last week, union members rejected a pay offer of a 5.7% increase.
Gary Nolan, managing director of First, South Yorkshire, said: "I am pleased the union has decided to suspend this action and we are optimistic the improved offer will be accepted and this dispute will soon be resolved."
http://news.bbc.co.uk/1/hi/england/south_yorkshire/3016382.stm