Putin said on Sunday that Russia had successfully tested its nuclear-powered Burevestnik cruise missile, a nuclear-capable weapon that it says can pierce any defence shield, and will move towards deploying the weapon.
Russia said the 9M730 Burevestnik (Storm Petrel) had flown for 14,000km.
Asked on Air Force One about the test of the missile, dubbed the SSC-X-9 Skyfall by the NATO military alliance, Trump said the United States did not need to fly so far as it had a nuclear submarine off the coast of Russia.
"They know we have a nuclear submarine, the greatest in the world, right off their shores, so I mean, it doesn't have to go 8000 miles," Trump told reporters, according to an audio file posted by the White House.
"I don't think it's an appropriate thing for Putin to be saying, either, by the way: You ought to get the war ended, the war that should have taken one week is now in ... its fourth year, that's what you ought to do instead of testing missiles."
Since first announcing the 9M730 Burevestnik in 2018, Putin has cast the weapon as a response to US moves to build a missile defence shield after the United States in 2001 unilaterally withdrew from the 1972 Anti-Ballistic Missile Treaty, and to enlarge NATO.
Asked about Trump's remarks, the Kremlin said Russia would be guided by its own national interests but saw no reason for the missile test to strain relations with the White House.
"Despite all our openness to establishing a dialogue with the United States, Russia, first of all, and the president of Russia, is guided by our own national interests," Kremlin spokesman Dmitry Peskov said.
"That's how it was, that's how it is, and that's how it's going to be."
The Kremlin said Russia was ensuring its own security by developing new weapons.
"There is nothing here that can and should strain relations between Moscow and Washington," Peskov said.
Trump has repeatedly spoken of moving US submarines to Russia's coast after remarks by former Russian president Dmitry Medvedev on the risk of war between the nuclear-armed adversaries.
It is rare for either side to discuss in public the location of nuclear-armed submarines.
Speaking about the Russian missile test, Trump said: "We test missiles all the time."
"They're not playing games with us and we're not playing games with them either," Trump said.
Ukrainian President Volodymyr Zelenskiy is expecting allies to put forward a concise peace proposal in the coming days to end the war, US news outlet Axios reported on Monday.
In an interview conducted on Sunday, Zelenskiy said the "coalition of the willing" - a loose alliance of 35 countries led by the United Kingdom and France, would be working on coming up with "some quick points" within "the next week or 10 days".
However, the Ukrainian president expressed scepticism that Putin would be ready to agree to the deal.
with DPA
