Speaking on his Telegram channel, Zelensky said Putin was using Ukraine as a "testing ground", and Russia was "so terrified" that it was "already using new weapons".
The US National Security Council, meanwhile, said "an experimental medium-range ballistic missile" had been used against Ukraine, adding that Russia probably only possessed a handful of these weapons and that they would not be a game changer in the war.
Putin said a "test" was successfully carried out on a non-nuclear hypersonic version of a ballistic missile and that the "target was reached".
"In response to the use of American and British long-range weaponry, on 21 November this year, the Russian armed forces carried out a combined strike on one of Ukraine's military-industrial complex sites," he said.
There is no way of counteracting this weapon, which attacks targets at a speed of 10 Mach, or 2.5-3km/s, he said.
And he warned the West that Russia was "ready for any developments. If anyone still doubts this, they shouldn’t. There will always be a response”.
Matthew Savill, director of military sciences at Rusi, a think tank, said available information about the Russian missile suggests something with a longer range than the Iskanders used so far in the conflict, which have a range of up to 500km (311 miles).
Intermediate-range ballistic missiles (IRBMs) - which Putin appears to have been describing - generally have ranges of between 3,000 and 5,500km.
Savill says the use of such a weapon may not have huge military significance but is symbolically important, coming on the back of Russia's revised nuclear doctrine which many see as a lowering of the threshold for the use of such weapons.
It is, he says, a not so subtle reminder that Russia has a wider arsenal of different and larger missile types and is ready to develop more.