Moscow’s defence ministry released footage showing a fighter jet taking off before the missile detaches, leaving flames blazing in its wake.
“The launch was normal; the hypersonic missile hit the preset target on the test site,” the ministry said.
Mr Putin described the Kinzhal missile as an “ideal weapon” when he announced the new arsenal of strategic weapons earlier this month,
The missile takes its name from a type of double-edged dagger and is said to be capable of travelling at 10 times the speed of sound.
Speaking in an annual state address on 1 March, the Russian leader claimed the missile’s speed “makes it invulnerable to current missile and air defence systems since interceptor missiles are, simply put, not fast enough”.
Moscow says the missile can deliver nuclear warheads at a range of more than 2,000 kilometres and could change trajectory mid-flight, “which also allows it to overcome all existing and…prospective anti-aircraft and anti-missile defence systems”.
The Kinzhal missile launched from a MIG-31 aircraft that took off from a military airfield in south-west Russia.
Other technologies touted by Mr Putin during the speech included a robot torpedo that Russia said could hit US port cities.
The Russian leader’s belligerent address raised the prospect of a new arms race. It came weeks after the Washington announced the US would expand its nuclear capabilities and signalled a hardening resolve against Moscow.
“Our strategy will ensure Russia understands that any use of nuclear weapons, however limited, is unacceptable,” said a Pentagon policy document.
Mr Putin said: “To those who in the past 15 years have tried to accelerate an arms race and seek unilateral advantage against Russia, have introduced restrictions and sanctions that are illegal from the standpoint of international law aiming to restrain our nation’s development, including in the military area, I will say this: everything you have tried to prevent through such a policy has already happened.
“No one has managed to restrain Russia.”
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However, US defence secretary James Mattis said the technology unveiled by Russia showed nothing that would change the Pentagon’s perspective.
He said: “I saw no change to the Russian military capability and each of these systems that he’s talking about that are still years away, I do not see them changing the military balance. They do not impact any need on our side for a change in our deterrence posture.”
Former defence secretary William Perry suggested Mr Putin’s “aggressive stance was almost entirely for domestic consumption and geopolitical posturing”.
In an article for Politico, he added: “Whether or not these new weapons work and whether or not they are available, they don’t change the basic deterrent posture or military capability of Russia.”