Owen Smith says he will try to stop Theresa May formally triggering Brexit unless she promises a referendum on the final deal or calls a general election to approve it.
The Labour leadership challenger said his party should not give the Tories a “blank cheque” on negotiations.
But rival Jeremy Corbyn said Parliament had to “work with” the result of the referendum.
Ministers said they would deliver on the “decisive” referendum verdict.
The UK voted to leave the EU by 52% to 48% in a referendum on 23 June but the manner and timing of the country’s departure remains uncertain.
The prime minister has said she will not begin the formal legal process of separation by activating Article 50 of the Lisbon Treaty this year, insisting that a “sensible and orderly departure” from the EU will take time.