Further negotiations between Unite and London Transit are due to take place.
If no agreement is made, some industrial action will go ahead and is likely to affect bus routes 13/N13, 23/N23, 31/N31, 218, 295/N295 and 452.
First Bus, which owns the two bus operators, said it had made an above-inflation offer.
A spokesperson for the firm said: “Our employees are at the heart of everything we do, and the above-inflation offer, which includes full back pay for all colleagues, demonstrates our commitment to supporting our people through the ongoing cost-of-living pressures while balancing the financial challenges we face as a business.”
The strike action was due to come after days of transport disruption for Londoners.
Thousands of members of the Rail, Maritime and Transport (RMT) union have been taking industrial action this week, which has crippled London Underground services, causing travel chaos in the capital since the walkout began on Sunday.