Speaking as he prepared to depart for a European trip in which he will meet the prime minister at the North Atlantic Treaty Organisation summit in Brussels and then make his first visit to the United Kingdom as president, Mr Trump insisted he got along with Mrs May "very well".
Speaking with a gaggle of reporters as he left the White House on Tuesday, Trump was asked if he considered Putin a friend or foe.
"While these countries have been increasing their contributions since I took office, they must do much more", Trump added.
"Dear @realDonaldTrump. US doesn't have and won't have a better ally than EU". "Europe far more than it does the US".
The President may come across the pond full of bravado but Mr Tusk issued this reminder: "Dear America, appreciate your allies - after all you don't have that many".
Donald Tusk's comments come in light on the problems emerging between the European Union and US.
Ahead of the meeting, European Council President Donald Tusk took Trump to task for "criticising Europe nearly daily".
Trump will visit Britain and meet Russian President Vladimir Putin in Finland's capital Helsinki after his stay in Brussels. "It is always worth knowing who is your strategic friend, and who is your strategic problem", Tusk says. Trump then heads to Helsinki to meet Putin.
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Tusk too urged the Europeans to increase spending as they have promised, but said: "Dear America, appreciate your allies, after all you don't have all that many". "Not fair to the US taxpayer", Trump tweeted earlier in the morning, calling the situation "Very Unfair!"
European officials have expressed hopes that member states can paper over their differences, but European Union President Donald Tusk delivered a blunt message to the U.S. leader on Tuesday. "Charge us big Tariffs (& Barriers)!"
He has also pointed the finger at European Union member states for not spending enough on defence - a long-standing complaint of USA presidents, including Barack Obama.
The increase from 1.46 percent of gross domestic product in 2017 underpins a general boost in defense budgets in Europe and Canada over the past four years. So we'll see. We're meeting with Vladimir Putin on Monday.
'When NATO has a Russian Federation council with the Ambassador from Russian Federation, we talk about the concerns that we have about Ukraine, the concerns that we have about Crimea, ' she said.
Trump has denied any collusion with Russian Federation.
This week's two-day summit, beginning on Wednesday at Nato's new headquarters in the Belgian capital, is expected to be dominated by USA demands for increased spending by other members of the 29-nation alliance.
"It's certainly going to be an interesting time with NATO", Trump said Tuesday morning as he headed to Brussels. "That's a fundamental inconsistency in the pro-NATO position", Mr. Desch said.