Labour MP Paul Flynn will lead a discussion over Donald Trump's state visit to the UK in the House of Commons on Monday (20 February).
"Trump should be invited to make an official state visit because he is the leader of a free world and UK is a country that supports free speech and does not believe that people that appose our point of view should be gagged," the second petition read.
But the more popular petition argued that the US president would "embarrass" The Queen. "Trump's well documented misogyny and vulgarity disqualifies him from being received by Her Majesty the Queen or the Prince of Wales," the petition said.
However, the government has rejected the calls to scrap the state visit invitation and Trump is expected to visit the UK in June.
"HM Government recognises the strong views expressed by the many signatories of this petition, but does not support this petition," the Foreign Office said in a statement.
"During her visit to the United States on 27 January 2017, the prime minister, on behalf of Her Majesty the Queen, invited President Trump for a state visit to the UK later this year."
The House of Commons debate coincides with new protests against Trump in London. The demonstrations are over the property tycoon's attempted travel ban.
The 90-day executive order prevented people from travelling directly to America from seven Muslim-majority countries, including Libya and Iraq. But federal US judges blocked its implementation.
The Stop Trump Coalition, co-founded by left-wing author and journalist Owen Jones, has organised demonstrations across the UK alongside One Day Without Us rallies, which aim to highlight the contribution migrants make to the British economy.
Meanwhile, House of Commons Speaker John Bercow is facing a motion of no confidence after he vowed to block Trump from addressing MPs in the Houses of Parliament.