Chief Secretary to the Treasury Danny Alexander has said he is "very confident" that the HS2 high-speed rail project will be delivered under budget.
Mr Alexander stressed that the Government would stick to the £42.6 billion budget for the rail project which will link London to the north as senior Labour figures appeared to cool on the plans.
His comments came ahead of a crucial week for HS2 when Labour support may be needed for the Government's proposals to continue their passage through the House of Commons as a number of Tory MPs are preparing to rebel and vote against a Bill which paves the way for the project.
Mr Alexander told the BBC's Andrew Marr Show: "The real cost is the budget that we set out in June this year - £42.6 billion. It hasn't changed at all.
"That number includes within it a significant amount of contingency.
"I'm very confident that, as we work through the project and deliver it, we will not just deliver it within that budget but, like the Olympic Stadium project, under budget too.
"That is something I'm working very, very hard to make sure happens.
"We are applying the same techniques we used to deliver the Olympic Park to the HS2 project."
Asked if he could guarantee that the final bill for HS2 would not be a penny more than the £42.6 billion budget, Mr Alexander said: "We have set that budget and we will stick to it."
Deputy Labour leader Harriet Harman played down comments by shadow chancellor Ed Balls comparing the project to the Millenium Dome.
Ms Harman said Mr Balls was asked about the Dome by a Mail on Sunday journalist and did not volunteer the comparison to the white elephant project.
The shadow chancellor told the newspaper the Dome was a mistake and said "I think you should learn from your mistakes".
This week Mr Balls said he still does not believe the case for HS2 has yet been made and claimed it would be "completely irresponsible" to sign it off until it had.
Ms Harman today stressed the need for the Opposition to keep a "strong eye" on the costs as well as the benefits and called on the Government to address people's concerns about HS2 rather than dismissing them.
Ms Harman told the Andrew Marr Show: "We absolutely support better north-south lines, we are in favour of rail infrastructure for commuters and also for long-distance travellers and freight but not at any cost and what Ed Balls is saying is we have to keep a strong eye on the costs as well as on the benefits.
"It's no good the Government simply complaining about people who are raising these issues, they should be addressing these issues, controlling costs and being properly analytical about the benefits that are available."
She went on: "(Mr Balls) was asked about the Millennium Dome, he didn't volunteer."
"Basically there's a question of costs and the benefits and you have to look at both of them.
"This is the responsibility that the Government have for spending public money, they have got to be absolutely sure that it's already a large amount of money - are the benefits justifying it, is it the right project?
"We have got to all the way along be encouraging the Government, instead of just cheerleading for this and blaming people who raise issues, saying this is a massive amount of public money, it's got to be well-spent."
Bob Crow, general secretary of transport union RMT, said the "political posturing" over HS2 was a smokescreen designed to delay investment in the railways.
Mr Crow claimed politicians were showboating while Britain falls behind other European countries on rail modernisation.
He said: " The latest outbreak of political posturing between Labour and the Tories over high speed rail is just another smokescreen designed to allow the politicians to delay investment in Britain's railways even longer while our overcrowded and clapped out services grind to a halt.
"Britain's rail system has been dumped in the slow lane for two decades under both main parties through the twin evils of private profiteering and political inertia on key investments like high speed rail. Today we see that they are back at it again and while the political class carry on showboating we slide further behind the rest of Europe on rail modernisation."
Labour former Cabinet minister Jack Straw said he was committed to HS2 as it would result in benefits to local rail services in the North and contribute to the economic regeneration of Britain.
The MP for Blackburn told Sky News's Murnaghan programme: " I am completely committed to HS2 and it will hugely benefit the north-west of England and indeed metropolitan Yorkshire as well.
"There are people who say if you have spent all this money, it is some billions, running a new high speed rail link to the north-west and to Yorkshire, then that is less money available for local improvements to the railway services in Lancashire and Greater Manchester and Yorkshire.
"I don't accept that because one of the reasons why the lion's share by far of all the money on suburban and urban transport has gone to London and the south-east in recent years is because they are so well-connected through inter-city services.
"So if we get this extra capacity into Manchester, into Leeds, into Sheffield, into Liverpool actually that will hugely benefit and trigger much greater usage of the railway services as well as helping this economic regeneration of the country and particularly this area."
Shadow energy secretary Caroline Flint told BBC1's Sunday Politics: "HS2 has never had a blank cheque from the Labour Party.
"(Shadow transport secretary) Mary Creagh has said if the prices are coming in too high then we will review our decision when we come back to vote on it next April.
"We have to look for value for money and we have to look at how it benefits the country."