Promoting the HS2 rail link on the basis of speed has been wrong, Transport Secretary Patrick McLoughlin has said.
Mr McLoughlin said cutting 20 minutes off journey times between London and Birmingham was "almost irrelevant".
But the transport secretary said the route was "essential for the future competitive edge" of Britain.
Shadow minister Maria Eagle reiterated support, saying the existing railway network was set to fail without HS2.
They spoke ahead of the publication of a Public Accounts Committee report on Monday which is expected to question whether HS2 is the most effective or economic way to respond to future rail demand.
The high-speed route would be between London and Birmingham before being extended to Manchester and Leeds.
The Treasury's top civil servant, Sir Nicholas Macpherson, has said there is "no blank cheque" for HS2.
Official estimates of the cost were increased by £10bn to £42.6bn earlier this year and there is opposition to HS2 in many communities along the proposed route.
Mr McLoughlin told the Sunday Times: "I think possibly the selling of the project was done wrong.
"The speed makes a difference to Manchester and Leeds, where you get an hour off the journey, but 20 minutes off the journey to Birmingham is almost irrelevant.
"It is nice but it is not important. It should always have been about capacity."
Ms Eagle indicated Labour still supported the scheme by saying there was no reason why it could not be built on time and on budget.
She urged ministers to "crack on" with the necessary legislation.
Ms Eagle said Labour leader Ed Miliband and shadow chancellor Ed Balls were both committed to the project.
"With the increase in traffic, the increased potential for freight, if we don't build this new north-south line then over the next 20, 30 years we are going to simply be, as decision makers, deciding how to preside over the failure of our railways," she told Sky News' Murnaghan programme.
Former Chancellor and Transport Secretary Alistair Darling and ex-Business Secretary Peter Mandelson have said they no longer support HS2 on the basis of cost.
They were both cabinet ministers in the Labour government that got the HS2 project under way.
Mr Darling warned of a potential "nightmare" on existing railways if HS2 is constructed.
HS2 chief executive Alison Munro has said she believes Labour is still strongly supportive of the scheme - but the Institute of Directors called on the government to abandon the project.
Speaking last weekend, Chancellor George Osborne said he was "passionate" about HS2 and that the Olympics showed the UK could deliver big projects to budget.
Richard Houghton, spokesman for campaign group HS2 Action Alliance, said: "In terms of capacity, there are many ways of increasing capacity across the network.
"Euston [planned to be used by HS2] is the second least-used line into London. So if you're going to fix capacity problems you wouldn't start there. If it's not about speed now, they need to reassess the route."
He added: "Maria Eagle has gone on record as saying she doesn't think the current route in London is acceptable."