Toninelli, a prominent member of the anti-establishment 5-Star Movement, also said he would not consider a decision to press ahead with the project as a political setback though his party has deeply opposed it for years.
The so-called TAV project is one of Europe's largest infrastructure projects, but Rome called for work to be frozen last year to enable an extensive review of its financial viability.
The issue is putting enormous strain on the ruling coalition because the far-right League wants it built, while Toninelli's 5-Star does not.
League politicians joined at a mass rally in Turin on Saturday to demand that work resume on the link and the row has the potential to split apart the eight-month-old coalition, which is beset by numerous difficulties as the economy approaches what could be its third recession in a decade.
In written answers to questions from Reuters, Toninelli said he believed 5-Star and the League would reach a deal on the TAV, adding that he would not consider it a political defeat if the multi-billion euro project ultimately went ahead.
"If we go ahead it means that it is worth doing it. I will have, myself, checked that people's money is not going to be wasted and therefore I will have done my best," he said. (Reporting by Stefano Bernabei, writing by Giselda Vagnoni Editing by Steve Scherer and Peter Graff)
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