Jeremy Corbyn has warned shadow cabinet ministers not to expect to stay in their jobs if they vote against starting the process of leaving the EU.
The Labour leader told ITV it was “impossible” for members of his top team to remain in place if they rebelled against a three-line whip.
Shadow Welsh Secretary Jo Stevens quit last week over the issue – other senior MPs say they will rebel.
Mr Corbyn has ordered all Labour MPs to support the bill triggering Article 50.
Labour backed the campaign to keep the UK in the EU in the referendum in June and many Labour MPs represent constituencies which voted for Remain.
But many seats which voted to leave the EU are also represented by Labour MPs.
Mr Corbyn says he understands the pressures on MPs in pro-Remain constituencies but has called on them to unite around the important issues.
His shadow home secretary Diane Abbott has said that, since a UK-wide referendum with a 72% turnout returned a vote in favour of withdrawing from the EU, it would “be very undermining of democracy” for MPs to vote against beginning the formal process of leaving.
Ms Stevens quit on Friday saying Brexit was a “terrible mistake”. Shadow minister Tulip Siddiq also quit last week saying she would vote against the EU (Notification of Withdrawal) Bill.
Two Labour whips, Jeff Smith and Thangam Debbonaire, who are in charge of party discipline, have also said they will rebel – though they have not resigned.
Another shadow minister Daniel Zeichner has said he will vote against the bill, as will other MPs including former Culture Secretary Ben Bradshaw.
Mr Corbyn told ITV’s Peston on Sunday: “There was no need for anyone to resign at this stage. It’s obviously impossible to carry on being in the shadow cabinet if you vote against a decision made after a very frank and very long discussion of the shadow cabinet earlier this week.”
Labour’s deputy leader Tom Watson has said divisions in the party will be handled sensitively and suggested some rebels could be back in senior roles “within months”.
The European Union (Notification of Withdrawal) Bill was introduced after the Supreme Court ruled that parliament – not just the government alone – must vote to trigger Article 50 of the Lisbon Treaty, which starts the formal process of the UK leaving the EU.
Prime Minister Theresa May has promised to begin the formal process of leaving by the end of March.
The bill is due to be debated by MPs on Tuesday – in a sitting that may last until midnight – and clear the Commons on 8 February, after which it will move to the House of Lords.
Labour has demanded changes including giving the Commons a vote on the final Brexit deal before European leaders or MEPs consider it.
The Liberal Democrats have vowed to oppose the triggering of Article 50 unless there is a guarantee of another referendum on the final Brexit deal that is agreed with Brussels, while the SNP has vowed to table 50 amendments to the legislation.