Transport Secretary Patrick McLoughlin has insisted that his budget of £42.6bn for the HS2 high-speed rail project has not changed.
It follows a report in the Financial Times that Treasury officials are preparing for an overspend of £31bn.
The Institute of Economic Affairs recently said it thought the project could cost more than £80bn.
Mr McLoughlin said he hoped the cost would be less than his current figure, which includes contingency money.
HS2, which stands for High-Speed 2, is intended to allow trains to run at 250mph (400km/h) from London to Birmingham from 2026, with branches to Manchester and Leeds via Sheffield planned by 2032.
Ministers have already had to revise the up budget for the project from the original £32bn, with extra tunnelling and infrastructure pushing up the cost.
The Financial Times report said the cost revision cited by Treasury officials took into account inflation and VAT over the project's 20 year completion and were in a sign of escalating concern within the department over the project,
Mr McLoughlin said: "I can't take account for what some people are supposedly saying in unattributed briefings.
"What I do know is that actually we have a very big problem as far as capacity on the railways is concerned.
"We have seen a 60% growth in freight on our railways. If we want to see more freight going on our railways we need to provide that capacity.
"The budget is £42bn and I announced that to Parliament. That has not changed. That is for building 351 miles of brand new railway."
He said there were always sceptics about big engineering projects, but pointed to Crossrail - a new east to west railway line across London, which is currently being built -as evidence that projects can be delivered on time and without spiralling costs.
He added that he would be looking to bring HS2 in under budget.
"I hope we can bring that figure down," he said.
"The figure I've given to Parliament did include a large amount for contingency, which is very necessary in big engineering projects."