Asked about Trump's comments, May said: "We're delivering on the vote of the British people to take back control of our money, our laws and our borders".
Timed with his arrival, members of Amnesty UK unfurled a banner reading "Donald Trump: Human Rights Nightmare" opposite the US Embassy.
Prime Minister May office said that she expected Donald Trump to discuss with President Putin issues like the Salisbury nerve agent attack on former spy Sergei Skripal and his daughter Yulia.
"I'd like to see them be able to work it out so it could go quickly", he said.
"It's important for us to send a powerful signal to those who are resisting and campaigning in America that we are standing in solidarity with them", Rehman said.
Mr Trump had joked earlier this week that his meeting with Vladimir Putin in the Finnish capital Helsinki on Monday "may be the easiest" part of his European trip.More news: 'Reckless': Trump escalates trade war with another $US200b in Chinese tariffs
However, despite the welcome from May, many Britons remain deeply opposed to Trump's visit.
Activists inflate a giant balloon depicting US President Donald Trump as an orange baby in north London on July 10, 2018 ahead of a demonstration in London to coincide with the visit of the US president.
Trump's victory in the 2016 presidential election shocked British diplomats in Washington and relations between May, a vicar's daughter, and Trump have been strained at times.
Other protests - including several "family friendly" gatherings - will take place at every place he will visit over the coming days.
Gorgeous said that they have worked closely with the Metropolitan Police and other march organisers - along with the people behind London's planned LGBTQ+ Community Centre, which are providing stewards - to co-ordinate the day.
While in Great Britain, Mr Trump will be running to a tight schedule which involves a high class dinner at Blenheim Palace, surveying United Kingdom military forces and visiting Chequers, the Prime Minister's official retreat in Aylesbury.More news: Giuliani: Cohen should cooperate with feds
Trump's trip coincides with a tumultuous week for May after two senior ministers resigned in protest at her plans for trade with the European Union after Britain leaves next March.
The two "Beasts" are among and huge motorcade of vehicles flown into Britain on two United States Air Force Boeing C-17 transport planes ahead of Trump's visit.
She listed Mr Trump's immigration policies, bans on some people entering the U.S., his foreign policies, and lack of support for taking action on climate change as having affects across the globe.
The bulk of the activity will take place in London, where people plan to gather first in Regent's Park outside of the US ambassador's house on Thursday and again across central London for a series of protests throughout the day on Friday.More news: Grayson Allen, Trae Young tussled during NBA Summer League game
The Metropolitan Police will be responsible for the protection and security of the United States president and will also try to ensure lawful protests can be staged.