Following the North Atlantic Treaty Organisation summit in Brussels, the President will travel to London for a four-day "working visit" that will include tea with the Queen, bilateral talks with May at her country house retreat and golf in Scotland.
From Belgium, Trump's trip will also take him to London, where Prime Minister Theresa May's government is in turmoil over her plans for exiting the European Union.
During his first meeting at the group's headquarters in Brussels previous year, Trump suggested that members who haven't been paying their fair share should be required to pay back dues.
President Tusk and President Juncker will attend two meetings at the NATO Summit, which starts in Brussels tomorrow (11 July).
It is these kinds of actions that make Mr Trump so risky.
Trump spoke after European Council President Donald Tusk addressed him in a statement, saying: "Appreciate your allies". As far as I'm concerned, a competitor.
"I think that getting along with Russian Federation, getting along with China, getting along with others is a good thing, not a bad thing", he added. US officials said the two sides this time would be discussing Russian election meddling, Russia's incursions in the Ukraine and involvement in Syria.
The meeting will be closely watched to see whether Trump will rebuke or embrace Putin, who has repeatedly denied the allegations of election meddling, in spite of evidence to the contrary.
Diplomats fear a rancorous meeting in Brussels could undermine efforts to show unity in the face of the growing threat on the alliance's eastern flank, particularly with Trump set to meet Putin in Helsinki a few days later.
"Certainly, the president has been very plainspoken about asking our allies to do more", Hutchison said from Brussels, noting that other former presidents, including Bill Clinton, George W. Bush, and Barack Obama, did the same. He also has long criticized Merkel for her 2015 decision to admit more than 1 million asylum seekers from Syria and elsewhere, warning that they were a proverbial Trojan horse who could destroy Europe's way of life.
'And the president is going to take those same messages to president Putin. "It's very clear, and he's been very direct about the Europeans needing to do more for their own security". "Many of these nations owe massive amounts of money from past years, and not paying in those past years", Trump told the leaders of member countries.
'And then of course in the eastern part of Ukraine there is a lot of trouble that has been fomented by Russian forces.
"Secretary of Defense [James] Mattis is supportive of NATO, the U.S. Ambassador to NATO, Kay Bailey Hutchison, is very supportive".
Trump has asked Europe to lower tariffs on American-made cars and other products and to buy American liquid gas.