Shadow transport secretary Maria Eagle said her party's backing depended on costs being kept under control for the high-speed route linking London to Manchester, Birmingham and Leeds.
The development comes after former Labour Chancellor Alistair Darling attacked the rising costs.
The comments came amid growing speculation over the opposition's stance on the scheme.
The leadership insists it still believes HS2, which aims at providing 225mph trains linking England's north and south by 2026, is vital.
Last week, shadow chancellor Ed Balls warned he would not write a "blank cheque" for the scheme.
Ms Eagle said: "I am not willing to see this project start draining money from other vital rail projects - it's got to be delivered within the current budget.
"Nobody who is delivering it should be under any illusions that I will allow it to go up and up. That would put our commitment to it at risk. It shouldn't be going up above that £50bn cap."
Ministers have estimated the cost, including rolling stock, will be around £50bn. However, other research has suggested the final bill for the project could reach £80bn.
Treasury officials are said to be privately working on a figure of £73bn.
Transport Secretary Patrick McLoughlin said last week David Cameron remained behind HS2, and expressed confidence there was still a cross-party consensus in favour.
Alison Munro, who is chief executive of HS2, said: "The costs of HS2 are firmly under control and we fully intend to deliver Britain's new high-speed rail network within the £42.6bn budget set by the Government.
"Passenger numbers continue to grow on our main north/south rail arteries and the time when we reach capacity crunch is approaching.
"There is no alternative that delivers the benefits of HS2."