Chancellor George Osborne has welcomed Sir David Higgins' recommendations for HS2, but warned there will be "no increases" in spending on the £50 billion poject.
Mr Osborne described the high-speed project as "essential to the future of this country".
However, he cautioned: "We must be conscious of the price, and there will be no increases to the overall spending envelope set for HS2 at the last spending review."
Earlier today, Shadow Transport Secretary Mary Creagh said there would be no "blank cheque" for the project.
Ms Creagh told BBC Radio 4's The World At One that Labour would be supporting the hybrid bill due to come before parliament but argued that the project had "suffered from mismanagement".
Plans to speed up the development of HS2 and extend it to the north more quickly have been backed by the government.
Asked whether the coalition would take action to accelerate the passage of the HS2 Bill through Parliament, Prime Minister David Cameron's official spokesman said: "We want it to proceed as quickly as it can, but it is obviously a very lengthy Bill."
Earlier today, Transport Secretary Patrick McLoughlin said Sir David Higgins' proposals for HS2 had the "strong support" of the government.
The government has also scrapped a proposed £700m scheme to link HS2 with the existing HS1 route to Brussels.
The government will instead look at other ways of linking HS2 with the continent.
HS2 link requires too many compromises in terms of impacts on freight, passengers and the community in Camden, says Transport Secretary.Read the full story ›
HS2 contingency savings cannot be guaranteed, the project's chairman has told ITV News' Deputy Political Editor Chris Ship:
HS2 boss Sir David Higgins says the high-speed rail project needs support across the political divide if it is to succeed, ITV News' Deputy Political Editor Chris Ship reports.
Speaking on the BBC's Andrew Marr show yesterday, Shadow Chancellor Ed Balls said: “I hope he [Sir David] will show he has got the costs down and got a grip on this project. If he doesthat, we will support this at second reading in the next few weeks.”
However, today's report on the project offered a number of recommendations but no new cuts.
The introduction of HS2 will "transform" service on existing train lines, Network Rail says.
Paul Plummer, group strategy director at the rail authority, said: "HS2 will sit at the heart of Britain's transport network, allowing us to reshape the railway in a way that incremental improvements simply cannot.
"That's why we welcome the report's recommendations and its call for an integrated approach to planning and operating the railway," he said.
Mr Plummer added: "The step-change in capacity that HS2 enables across the network as a whole will transform the service on existing lines, creating the space we need to meet growing demand and deliver new and better connections."
The north will face a "lost decade of growth" if recommendations to extend the early phase of HS2 are not accepted by politicians, a major rail union says.
Following Sir David Higgins' call to extend phase one of the project to Crewe, TSSA leader Manuel Cortes said: "Sir David is absolutely right - we cannot, as a country, take the slow line to a high-speed rail future.
"We need to make sure that the north benefits as quickly as the Midlands and the South from this huge investment.
The alternative, he said, is a "lost decade of growth while the South East powers ahead of the rest of the country with the lion's share of the budget".
"The £50 billion investment must benefit the whole country if it is to help re-balance the economy," Mr Cortes added.
Demand on Britain's rail service is "growing at 5%" every year, the chief executive of HS2 told Daybreak.
Sir David Higgins said a completed HS2 line would cure a multitude of economic woes, including creating jobs, lure more businesses to the north and help create more space for passengers.
"No new railway lines north of London in 100 years - why should we put up with that? It's not fair on jobs that are created in the region."
HS2 is about "rebalancing the economic geography of the country" and creating transport links to mend the north-south divide, the shadow transport secretary told Daybreak.
Mary Creagh was optimistic about the future of HS2 and said the rail link should be "integrated" with the rest of the network so passengers would be able to travel east-to-west, as well as north-to-south.
The mother of a severely disabled son has told Daybreak how HS2 will force her "to restart our life again" if they are forced to move out of the home which was specifically adapted to meet her son's needs.
Thelma and her son Alexis, who live in the town of Northwich in Cheshire, are potentially in the pathway of HS2 and may have to move - something that will put a severe amount of stress on the pair.