Mr Alexander stressed the Government would stick to the £42.6 billion budget for the rail project which will link London to the north as top Labour figures appeared to cool on the plans.
His remarks came before a key week for HS2 when Labour support may be needed for the Government's proposals to continue through the House of Commons as a number of Tory MPs prepare to vote against a Bill paving the way for the project.
Mr Alexander said: "The real cost is the budget that we set out in June this year - £42.6bn. It hasn't changed at all. That number includes within it a significant amount of contingency.
"I'm very confident that, as we work through the project and deliver it, we will not just deliver it within that budget but, like the Olympic Stadium project, under budget too. That is something I'm working very, very hard to make sure happens. We are applying the same techniques we used to deliver the Olympic Park to the HS2 project."
Asked if he could guarantee the final bill for HS2 would not be a penny more than the £42.6bn budget, Mr Alexander said: "We have set that budget and we will stick to it."