Scrapping HS2 beyond Birmingham would represent a "huge betrayal" of the Midlands and the North, Transport Secretary Chris Grayling has said.
He described reports that the second stage of the project "might not happen" as "completely inaccurate".
There is growing speculation that the scope of HS2 will have to be reduced if it is to avoid exceeding its £55.7 billion budget.
In November, Mr Grayling reportedly told rail industry figures that the extension of the railway north of Birmingham was "not in the bag" and the project "still needs support if it is to definitely go to Leeds".
The Parliamentary bill for Phase 1, between London and Birmingham, was passed in February 2017, while Phase 2a between Birmingham and Crewe is going through Parliament.
But legislation needed for Phase 2b, extending the railway to Manchester and Leeds, has been delayed.
The Department for Transport has previously said this is to improve HS2's connectivity with east-west rail lines across the North.
On Tuesday a former HS2 chairman claimed the railway should have been given a different name because its capacity is more important than its speed. Sir Terry Morgan, who resigned from HS2 Ltd last month, told the House of Lords Economic Affairs Committee: "I think most people regret actually calling it HS2."