HS2 chairman Allan Cook has said not completing the £56bn railway to the north of England would be a "complete betrayal".
Cook, who was appointed as chairman following the departure of former Crossrail head Terry Morgan, told MPs on the Transport Select Committee that HS2 was looking at "all options" to keep the project within budget but rejected suggestions that it could stop at Birmingham.
HS2 will be split in two phases: phase one will link London to Birmingham, while phase 2 will stretch from Crewe to Manchester, and the West Midlands to Leeds.
In recent months there have been reports that the second phase of the railway could be scrapped in a bid to save costs. Last year, transport secretary Chris Grayling admitted the second part of the railway was "not in the bag".
Cook said the "ultimate challenge" for HS2 was to deliver the programme in terms of costs, schedule and scope.
But he said he had had "no indication" from the Grayling that more money would be set aside for the project in the spending review later this year.
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Earlier this year HS2 chief executive Mark Thurston caused controversy when he admitted at a parliamentary meeting that the 56bn project could be forced to run fewer trains at slower speeds to keep a grip on costs – prompting House of Commons leader Andrea Leadsom to question whether there was still a "business case" for HS2.
HS2 has insisted the project will be delivered on time and on budget.