David Davis has warned Conservative MPs not to "tie the Prime Minister's hands" by backing amendments to the Article 50 bill this week.
The Brexit secretary told the BBC's Andrew Marr that doing so would prompt concerns among voters that Parliament intends to reverse the decision to leave the EU.
He said: "It's inconceivable to me that there wouldn't be a vote on the outcome.... We are going to do that.
"Please don't tie the Prime Minister's hands in the process of doing that for things which we expect to attain anyway."
Pressed on whether Parliament would get a meaningful vote, he replied: "What we can't have is either House of parliament reversing the decision of the British people.
Writing exclusively for the Telegraph, the Brexit Secretary also said that putting promises over leaving the EU into law creates a “greater risk of legal action".
He warns that Theresa May would be negotiating with “one hand tied behind her back” if MPs approve two changes to the law proposed by Lords.
Mr Davis also says that protecting the rights of EU citizens in the UK without reciprocal promises would plunge more than a million Britons abroad into “uncertainty”.
At 137 words, the Bill which enables the Prime Minister to notify of our withdrawal from the European Union is one of the shortest on record
“There will be many opportunities for Parliament to debate the ins and outs of our negotiation of a new partnership with the EU, and influence the outcome,” he writes.
“But attaching conditions to a Bill that simply allows the Prime Minister to start the process of implementing the referendum result is emphatically not the way to do it.”
The shot across the bows comes ahead of a historic week in Parliament that is expected to see Britain's withdrawal from the EU approved by MPs and peers.
Mrs May is preparing to formally start negotiations as early as Tuesday in a landmark moment in Britain’s modern history, dubbed “independence day” by supporters.
However, before that can begin, MPs must vote on Monday on whether to make two amendments to the legislation giving the Prime Minister the power to start Brexit.
The first would demand proposals are published within three months to protect the rights of all EU citizens currently in Britain. The second would give MPs and peers a “meaningful vote” on the final Brexit deal - effectively a veto, as the UK's departure could not happen without a parliamentary vote.
Both are being opposed by the Government, but pro-EU Tories are rallying support privately behind both changes. Only about 30 Tory MPs are needed to back the changes for them to pass, given opposition parties support them and the Conservatives have such a slim majority.
Tory whips are so concerned about the vote that cabinet ministers have been forced to cancel foreign trips to make sure they are in Parliament.
Conservative whips have effectively banned foreign trips by refusing to approve any “slips”, which give MPs permission to be away from Parliament.
At least two ministers planning visits abroad have been forced to cancel their plans because of the tight restrictions, the Sunday Telegraph has learned.
“It is impossible to get away at the moment. If this carries on, it increases the incentive to go for an early election,” said one minister.
Mr Davis, the Secretary for Exiting the European Union, uses the piece for the Telegraph to warn off Tory MPs considering supporting either amendment.
“At 137 words, the Bill which enables the Prime Minister to notify of our withdrawal from the European Union is one of the shortest on record,” Mr Davis writes.
“Yet it has generated many hours of debate in Parliament. That's to be expected, and a good thing: the decision taken by the people of the UK on June 23 was, after all, the most momentous of my lifetime.
"However, by a majority of four to one, the elected House of Commons accepted the simple, straightforward and clear aim of the Bill.
"That is to allow the Prime Minister to implement the outcome of the EU referendum, while respecting the judgment of the Supreme Court that this should be authorised by legislation. No more, no less.
“MPs passed the bill quickly and unamended. They accepted that the majority of voters, however they voted in the referendum, want the Prime Minister to be able to get on with the job, with no strings attached.”
Mr Davis addresses the arguments of critics head-on. He says making promises to EU citizens in the UK without achieving a reciprocal promise for Britons abroad “risks exposing UK citizens in the EU to a long period of uncertainty”.
He says calls for a “meaningful vote” on the final Brexit deal is actually a “veto” and notes that the Prime Minister has already verbally committed to a vote.
He also raises the spectre of Brexit ending in the courts if changes are passed, saying: “The more conditions that are attached, the greater the risk of legal action down the line.”
Mr Davis finishes: “Parliament will be properly engaged and involved throughout. It should not send our Prime Minister into this vital negotiation with one hand tied behind her back.”
In the run-up to the vote, pro-EU Tory MPs have rejected claims the amendments would undermine Mrs May’s negotiating stance as “absolute rubbish”.
One Tory rebel said: “What we will not have is this ideological claptrap for hard Brexiteers who want take us out of the EU without a deal.
“They are, as far as we are concerned, the awkward squad and have a tendency to push the government into public statements. That is where the tension comes in.”
Europhiles on the Tory backbenches say there is more support for the “meaningful vote” amendment than that securing the rights of EU citizens.
However, politicians on all sides do not expect enough Tory MPs to back either of the changes, with the number of rebels possibly as low as single figures.
If the Commons approves the Article 50 Bill by Monday afternoon and the Lords later that day, Mrs May will be free to start Brexit on Tuesday.
No 10 is preparing a “moment” to mark the historic notification of withdrawal, with a letter sent to Brussels and a speech.
Aides to the Prime Minister insist that no date has been picked for the triggering of Article 50, although Mrs May has until the end of March to do so. That will begin a two-year negotiation period before Britain formally leaves the EU in 2019.
In a separate development, the cross-party Commons Foreign Affairs Committee today calls on ministers to start preparing for Britain not securing a deal with the EU.
The report warns of “mutually assured damage” if no Brexit deal is struck during the two-year negotiation that would keep trade barriers low and secure security cooperation.
Crispin Blunt, the Tory chairman of the committee, said: “The possibility of ‘no deal’ is real enough to require the Government to plan how to deal with it.
"But there is no evidence to indicate that this is receiving the consideration it deserves or that serious contingency planning is underway.
“The Government has repeatedly said that it will walk away from a ‘bad’ final deal. That makes preparing for ‘no deal’ all the more essential. Such preparation reinforces that stance.
“Last year, the Committee described the Government’s failure to plan for a Leave vote as an act of gross negligence. This Government must not make a comparable mistake.”