But asked at Prime Minister's Questions by Labour MP Angela Eagle if her move would mean a Commons vote before invoking Article 50, Mrs May replied: "The idea that Parliament somehow wasn't going to be able to discuss, debate, question issues around (Brexit) was frankly completely wrong".
The battle over Brexit reaches the High Court on Thursday in a legal challenge to Prime Minister Theresa May's right to start negotiations for Britain to leave the European Union.
In a speech stressing Europe's red lines in Brexit negotiations due to start before April, Tusk said British Prime Minister Theresa May has signaled a "de facto will to radically loosen relations with the EU" by pledging to give priority to regaining United Kingdom sovereignty over immigration.
Labour is expected on Wednesday to try to exploit the government's discomfort with a debate on a motion calling for "a full and transparent debate" to allow the Commons to "properly scrutinise" the government's plans before Article 50 is activated.
The case reflects growing pressure from MPs themselves, led by the main opposition Labour party, for a vote on the terms of Britain's exit over fears of an abrupt departure from the single market. May also appeared to signal that her government would prioritize controls on immigration over access to the European single market, an approach informally called a "hard Brexit".
Shadow Brexit Secretary Sir Keir Starmer said: "There is a mandate for exit - there's not a mandate for the terms. The majority of remain voters do not want the democratic process in the referendum bypassed by MPs", one Conservative who supported remain but now favors triggering Article 50, said in response to the anonymous survey.
May has said she will trigger the Brexit process by the end of March 2017.
"We've always said that parliament has an important role to play, and the amendment reflects that", her spokeswoman said.
It looks like Britain is careening head-first into a "Hard Brexit", which would see it restrict freedom of movement but lose Single Market access.
Won't screen films with Pakistani artistes, say cinema owners
It, however, had said that "Ae Dil Hai Mushkil", "Raees" and other films starring Pakistani actors, which have completed production, would not be affected.
The Labour leader said the PM offered "no strategy for negotiating Brexit and offers no clarity, no transparency and no chance of scrutiny of the process for developing a strategy".
He said the government was wrong to suggest that Miller was trying to change the outcome of the June 23 referendum in which 52 percent voted to leave the European Union and 48 percent to remain.
Lawyers go to the High Court on Thursday to pursue a judicial review, claiming the Government can not trigger Article 50 without Parliament's permission.
"But we're not going to be getting into a running commentary about the details of this negotiation".
Mrs May has insisted she would not give a "running commentary" over negotiations with European Union leaders.
The government says a vote in Parliament is not required.
But she stopped short of allowing a formal vote on its strategy before Article 50 is invoked, as some Labour lawmakers had called for.
"I hope ministers will now listen to MPs on all sides and give Parliament a vote on the terms of their Brexit negotiations".