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.

Discussions are set to focus on Syria and Iran, particularly the nuclear deal bitterly opposed by Mr Netanyahu.
Mr Cameron said the UK "remains staunch" in its "defence of Israel's right to exist and to defend itself".
Pro-Palestinian campaigners have denounced Mr Netanyahu's visit.
There were angry confrontations outside Downing Street on Wednesday between protesters demanding Mr Netanyahu's arrest for what they say amount to war crimes in Gaza and pro-Israel activists.
Although a petition calling for the Israeli PM's arrest secured enough signatures to be considered for a debate in Parliament, the bid was rejected earlier this week because "visiting heads of foreign governments... have immunity from legal process, and cannot be arrested or detained", the UK government said in a statement.
Arriving in Downing Street, Mr Netanyahu said: "The Middle East is disintegrating under the twin forces of militant Islam - militant Sunnis led by Isis [Islamic State] and militant Shiites led by Iran.
"I believe that we can co-operate in practical ways to roll back the tide of militant Islam both in the Middle East and in Africa."
The Israeli premier also said he was "ready to resume direct negotiations with the Palestinians with no conditions whatsoever to entering negotiations... immediately".
Talks between Israel and the Palestinians broke down in April 2014.
Mr Cameron praised the "close relationship between Britain and Israel" and the "growing economic and commercial ties" between the countries.
He said he wanted to talk about the "enormous important global threats" in particular so-called Islamic State.

Bath boss Mike Ford announced in October that the former Scarlet star, 28, was taking a sabbatical.
"We agreed to sign Rhys on the basis that he did not play international rugby," said Ford. "He's now decided that he wants to play again."
Dan Biggar was the first choice No 10 during the World Cup earlier this year as Wales reached the quarter-finals.
Priestland has won 40 Test caps and replaced Biggar during the last-eight loss to South Africa on 17 October.
Ford explained that Priestland's U-turn was the reason Bath had signed utility back Dan Bowden from New Zealand.
But the coach added: "We're hoping Rhys will be with us for the two years of his contract and possibly beyond that."
Ford wanted Priestland to act as cover for his son, George, who is expected to be part of England's Six Nations squad.
The leader of England's biggest union has warned that a strike by bus drivers in Oxford over pay could spread.
[NEXT_CONCEPT]
Action is needed to stop the Middle East "disintegrating" under the threat of militant Islamists, Israeli PM Benjamin Netanyahu said at the start of talks in London with David Cameron.
[NEXT_CONCEPT]
Wales fly-half Rhys Priestland has reversed his decision to take an 18-month break from international rugby.