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More than a million people have so far called for the visit to be cancelled.
The petition, if accepted by Parliament, will force MPs to debate the motion: "Prevent Donald Trump from making a State Visit to the United Kingdom."
However, Theresa May insisted the visit would still go ahead, no matter how many people signed a petition against it.
"The petition has been signed by however many people have signed it," her spokesperson said.
"It will be a matter for Parliament now whether it is debated [but] what we've been very clear on is that we have extended this invitation to the President and it has been accepted and we will proceed with a state visit."
London mayor Sadiq Khan called on Monday for the offer of a state visit to be withdrawn until Trump's Muslim ban is cancelled.
"We must now rescind the offer of a full state visit for President Trump - until this ban is lifted," Khan wrote in the Evening Standard.
"I don't believe the people of London will support rolling out the red carpet until this happens."
The United Nations' High Commissioner for Human Rights on Monday described Trump's travel ban as "mean-spirited" and illegal under international human rights law.
Zeid Ra'ad al Hussein said: "Discrimination on nationality alone is forbidden under human rights law. The US ban is also mean-spirited, and wastes resources needed for proper counter-terrorism."
Thousands of people are expected to protest against the ban outside Downing Street tonight.