George Osborne has told the BBC he is "passionate" about the multi-billion pound high speed rail project, despite rumours that the costs are spiralling.
The chancellor said he had set a £42bn budget with a £14bn contingency fund- and the Olympics showed that the UK could deliver big projects to budget.
His predecessor, Labour's Alistair Darling, is among those sceptical about whether the project is worth the cost.
HS2 Ltd's boss Alison Munro says it is not true that costs are out of control.
The project's first phase would see 225mph trains running on a new railway line to be built between London and the West Midlands by 2026. A second phase would see the line extended further north, with branches to Leeds and Manchester by 2033.
Labour's front bench says it is still behind the project, but last week placed a £50bn cap on costs.
However Lord Mandelson and Mr Darling - both cabinet ministers in the Labour government that approved HS2's initial phase in principle - say they have since changed their minds, after estimated costs rose from £34.2bn to £42.6bn.
Asked whether he had a ceiling on costs, beyond which he would not support HS2, Mr Osborne told BBC One's Andrew Marr Show: "We have set the budget for £42bn for the construction costs. That includes, by the way, a big contingency.
"As we demonstrated with the Olympic Games, we can deliver these big projects actually sometimes under budget."
"I think we have got a good budget, which has got a very big contingency in it, we've set a budget.
"I'm passionate about this project because time and again, we have this debate in our country about how we're going to bring the gap between north and south together, about how we're going to make sure that our growth is not just based on the City of London.
"High Speed 2 is about changing the economic geography of this country, making sure the North and the Midlands benefit from the recovery as well."
Mr Osborne also defended his "Help to Buy" scheme, which effectively underwrites 95% mortgages and allows people buying newly built homes in England to proceed with a deposit of just 5%.
Asked if low interest rates could fuel a new housing bubble, he said too much of the media and political debate was focused on what happened in London.
"Outside the centre of London, actually there's not some housing boom or some dramatic increase in house prices. There are many, many thousands of families watching this programme who can't begin to afford the mortgage deposits that are required to buy a home. They aspire to own their own home, that's a noble aspiration and I want to help them."
HS2 has had the backing of all three main party leaders since its conception - despite strong opposition among some backbench MPs.
But Labour's shadow chancellor, Ed Balls, has said he will not write a "blank cheque" for HS2 and party leader Ed Miliband has said he is a supporter of the project but it must be "value for money".
However HS2 Ltd chief executive Ms Munro has said talk of costs spiralling out of control are "simply not true".
"The current budget is £42.6bn for the infrastructure and £7.5bn for the rolling stock.
"We are absolutely determined, and the government is too, now to manage the project within that cost envelope."
Supporters of HS2 argue that aside from shorter journey times, the main argument in favour of the project is the need to greatly increase passenger capacity.
Construction on the London-West Midlands phase is expected to begin around 2017, once Parliament has approved the necessary powers - probably in 2015.
The onward legs to Manchester and Leeds could start being built in the middle of the next decade, with the line open by 2032-33.