Asked if his patience with Putin had run out, Trump said: "Yeah. It's sort of running out and running out fast."
In an interview with Fox News, Trump said he had long had a good relationship with Putin but expressed frustration at his failure to end the war.
"We're going to have to come down very, very strong," he said.
Trump said sanctions on banks and oil were an option, along with tariffs, but European countries also needed to participate.
"But I've already done it. I've done a lot," Trump said, noting that India - one of the biggest buyers of Russian oil - was facing a 50 per cent tariff on its exports to the United States.
"That's not an easy thing to do. That's a big deal and it causes a rift with India," he said.
"And remember this, this is a Europe problem, much more than our problem."
The NATO military alliance on Friday launched an operation named Eastern Sentry to bolster the defence of Europe's eastern flank in response to Russian drone incursions into Polish airspace earlier this week, Secretary-General Mark Rutte said.
"We must, as NATO, make clear our resolve and our ability to defend our territory, and that is exactly what Eastern Sentry is designed to do," Rutte told a press conference at NATO headquarters in Brussels.
"This military activity will commence in the coming days and will involve a range of assets from allies including Denmark, France, United Kingdom, Germany and others," he said, standing beside NATO's top commander, US Air Force General Alexus Grynkewich.
Rutte said NATO was still assessing the possible intent behind the incursion, which led to Polish and allied NATO forces shooting down several drones - the first time NATO has taken such action since Russia's 2022 invasion of Ukraine.
But he said Russia's action had been "reckless and unacceptable," whether intentional or not.
Russia said its forces had been attacking Ukraine at the time of the drone incursions and that it had not intended to hit any targets in Poland.
Polish officials have rejected that explanation, saying the incursion was a deliberate attack.
Grynkewich said Eastern Sentry was designed as a flexible and integrated operation to bolster defences along NATO's entire eastern flank, which stretches from the Baltic states in the north to Romania and Bulgaria in the south.
"Poland and citizens from across the alliance should be assured by our rapid response earlier this week and our significant announcement here today," he said.
NATO already has substantial forces in eastern Europe, including thousands of troops.
It did not put a figure on how many additional troops would be involved in the new operation.
Its announcement detailed a modest number of additional military assets - including two F-16 fighter jets and a frigate from Denmark, three Rafale fighter jets from France and four Eurofighter jets from Germany.
But Grynkewich said the new operation was also about adopting a more flexible approach to defending the eastern flank as a whole, rather than just having more static forces devoted to a particular area.
"Across the eastern flank, we will constantly adjust and change our posture in a manner that keeps the adversary off guard but also responds to specific threats as we see them emerging," he said.
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