Len McCluskey joined Unite members from the Oxford Bus Company on the picket line earlier, and warned seven other bus depots run by the Go Ahead Group could be affected.
Drivers have walked out on two separate days angry that they were only paid for three bank holidays over Christmas.
Oxford Bus Company said its drivers were among the highest paid anywhere.
'Incredible resolution'
Mr McCluskey warned that unless the issue was resolved, bus services in London and other parts of the country could also expect industrial action.
He said: "I sincerely hope that the Oxford Bus Company pays heed to the incredible resolution of Unite's members.
"They are in no mood to roll over, and they know that they have the full support of their union in their corner.
"Unless the company restores facility time and starts treating our members with respect I will have no option but to take this dispute to every Go Ahead depot in the country."
But Phil Southall, the managing director of Oxford Bus Company, said it was continuing to run about 90% of services.
He added: "This is purely a local issue to Oxford about the Christmas and New Year bank holidays.
"We were willing to agree to suspend any legal action, reinstate the recognition agreement and the stand down time at Unite's request if strike action was called off and no further dates announced.
"It is becoming clearer that this strike is about Unite the union and not about our drivers' and engineers' best interests."
The Go Ahead Group says its operations include eight regional bus companies, one of which is in London, where it provides about 24% of services on behalf of Transport for London.
The leader of England's biggest union has warned that a strike by bus drivers in Oxford over pay could spread.