Earlier, the Foreign Office rejected the petition calling for Mr Trump's trip later this year to be downgraded, stripping it of the trappings of a state visit.
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In a statement, the Foreign Office said the Government "recognises the strong views expressed by the many signatories of this petition, but does not support this petition".
Support for the call to downgrade Mr Trump's visit because it would be "embarrassing" for the Queen snowballed after he imposed a travel ban on nationals from seven mainly Muslim countries.
The Government was compelled to reply to the petition because it garnered more than 10,000 signatures.
MPs will debate it in the House of Commons on Monday alongside a rival 300,000-strong petition in support of the state visit after they both reached the 100,000 signatures threshold to be considered for discussion in Parliament.
Responding to the anti-state visit petition, the Foreign Office said the invitation reflected the importance of the relationship between the US and the UK.
"HM Government believes the President of the United States should be extended the full courtesy of a state visit," it said in a statement.
"We look forward to welcoming President Trump once dates and arrangements are finalised.
"HM Government recognises the strong views expressed by the many signatories of this petition, but does not support this petition."
Meanwhile, outgoing Metropolitan Police Commissioner Sir Bernard Hogan-Howe has warned ministers must make extra resources available for policing the visit, which is expected to trigger mass protests.
"I'm sure the Government recognises the economic value of a safe capital and won't put my successor into the position of having to choose between this and keeping our neighbourhoods safe," he said in a valedictory speech to the Royal United Services Institute.
Mrs May has been criticised for offering Mr Trump a state visit too soon in his already highly controversial presidency.
Barack Obama only received an invitation after 758 days, while it took 978 days before his predecessor, George W Bush, was offered a state visit, compared with seven days for Mr Trump.
The backlash against the visit has also caused controversy in Parliament, where Commons Speaker John Bercow is facing calls to resign after branding Mr Trump "racist" and "sexist" and effectively banning him from addressing MPs and peers in Westminster Hall during the trip.
The travel ban, which sparked mass protests in the UK and around the world, has since been suspended after two states - Washington and Minnesota - sued and a federal court rejected a US government appeal.
The Stop Trump campaign has called protest rallies around the country for February 20, when the petition will be debated by MPs, and is promising "the biggest demonstration in British history" if the visit goes ahead.
A campaign spokesman said: "Theresa May has shown her contempt for people asking for her to take a stand against racism, and sided with a bigoted megalomaniac instead."