Jeremy Corbyn faces a fresh split in the top levels of his party after imposing a three-line whip on his MPs to back the Article 50 legislation.
Would-be rebels would normally be expected to resign from frontbench posts if they refuse to follow the Labour leader's position in approving the Government's Bill next week.
Mr Corbyn said he understood the "pressures" facing his MPs but urged the party to unite and make sure the legislation goes through the Commons.
Labour confirmed there would be a three-line whip for the Bill's second reading, the first Commons test for the legislation which will allow Theresa May to formally start the Brexit process.
Mr Corbyn said: "I fully understand the pressures and issues members are under - those who represent Leave constituencies and those who represent Remain constituencies.
"Labour is in the almost unique position of having MPs representing constituencies in both directions, and very strongly in both directions.
"I say to everyone, unite around the important issues of jobs, security, economy, rights, justice, those issues, and we will frame that relationship with Europe in the future outside the EU, but in concert with friends, whether those countries are outside or inside the EU.
"That's the message we're putting out and I'm asking all our MPs not to block Article 50 and make sure it goes through next week."
Senior party sources had previously indicated that Mr Corbyn understood the "difficulties" facing Labour MPs in heavily pro-Remain constituencies.
Shadow education minister Tulip Siddiq has said she is ready to step down from her position if necessary to represent the views of her north London constituents, who voted overwhelmingly to Remain, while shadow business secretary Clive Lewis has said the Prime Minister's plans for Brexit are not in the best interests of his constituents or the country.
Asked whether they would face the sack if they voted against the whip, the Labour source said: "I would not assume anything about disciplinary action."
The source added: "What is normally expected of people will be expected of them."
The Labour leadership is expected to table five major amendments to the European Union (Notification of Withdrawal) Bill as it goes through the Commons.
Mr Lewis said he would vote for the Bill at second reading, but stressed that Labour would seek to amend the legislation to stop Mrs May using Brexit to "trash our rights".
"I have been clear throughout that I respect the result of the referendum and will, therefore, join my colleagues in voting for the Bill on its second reading," he said.
"However, Theresa May does not have a mandate to dictate the terms of Brexit without listening to the British people.
"The whole country should be involved in determining our shared future, which is why Labour has fought for the British people to have a say, through Parliament.
"Labour will seek to amend the Bill to prevent the Government using Brexit to trash our rights, public services, jobs and living standards while cutting taxes for the wealthiest."