The bill will become law once it receives Royal Assent from Queen Elizabeth II.
That would still leave May with time to trigger Article 50 on Tuesday, but any delays could make it Wednesday. They also dismissed calls for parliament to have a meaningful vote on any Brexit deal by 331 to 286 votes.
The speech also came as Scottish First Minister Nicola Sturgeon said she meant to call an independence referendum between the fall of 2018 and the spring of 2019.
"We will need to negotiate with the European Union in a way that shows our openness and our willingness to retain our strong bonds, because that will influence our relationship with the European Union as a bloc".
"So we will trigger Article 50 by the end of this month as planned and trigger an outcome that works in the interests of the whole of the United Kingdom".
Mr Verhofstadt said: "Since I've been appointed as the European Parliament's Brexit negotiator, I have also received numerous testimonies and letters of support from British people anxious about their future".
David Davis has rejected calls for the Government's Brexit Bill to include a clause giving Parliament the power to reverse Brexit, claiming it is "unnecessary" - despite having previously said that countries which can not change their minds "cease to be democracies".
Lesbian sex, violence and Charlize Theron: Atomic Blonde trailer and gallery
His work here helped land him the coveted gig directing the upcoming Marvel sequel Deadpool 2 for 20th Century Fox. Fittingly, people immediately compared Theron in Atomic Blonde to Keanu Reeves in the John Wick movies.
British citizens should be able to choose to keep various benefits of EU membership including the freedom of movement after Brexit, the European Parliament's chief negotiator has said. She has revealed little of her strategy for Brexit negotiations but has a long wish list - wanting to win a free trade deal, maintain security cooperation, regain control over immigration and restore sovereignty over British laws.
Mr Barnier had suggested that a Brexit bill would have to be paid upfront before negotiations with the Brussels bloc began.
Labour's Lady Hayter said the party accepted parliament's verdict and would instead look forward to trying to influence the next two years' of Brexit negotiations.
Even if Britain and the European Union enter negotiations with goodwill and the desire for a successful outcome, parliament's Foreign Affairs Committee say negotiations could stall, or be derailed, ending with no deal between Britain and the EU's 27 member states.
Bob Nei l l, another former Tory minister, said by phone on Saturday he's weighing how to vote and hopes May will give new assurances over Parliament's role.
In a statement issued following a meeting with United Kingdom prime minister Theresa May at Westminster Abbey, Muscat said that Malta will look to move any discussions in a direction that would be "in everyone's interests".
"Making an equivalent mistake would constitute a serious dereliction of duty by the present administration", they said in the report.