Moscow's military on Tuesday pledged a response to fresh Ukrainian air attacks inside Russia using US-supplied ATACMS missiles.

Ukraine firing the long-range missiles into Russia for the first time last week prompted a furious reaction from Moscow.

Russia's defence ministry on Tuesday said Ukraine had carried out fresh strikes on November 23 and 25 using ATACMS.

"Retaliatory actions are being prepared," it said in a post on Telegram, without elaborating.

The United States gave Ukraine permission to use the weapons to hit Russian territory earlier this month after months of requests from Kyiv.

In a rare admission, Russia said the fresh strikes had caused damage to military hardware and wounded some of its personnel on the ground.

A strike on the Kursk Vostochny air base wounded two servicemen, the defence ministry said, while a strike on an air defence battery damaged a radar system and also caused "casualties".

It said three of the five missiles fired in the first strike were shot down, while seven of the eight used in the second were destroyed.

Moscow rarely provides such specific details on Ukrainian aerial attacks and almost never admits missiles have reached their intended target.

The defence ministry also posted photos of what it said were the missile fragments, showing large casings with English-language inscriptions on the side.

The images could not be immediately verified.

The strikes come with tensions having ratcheted up dramatically in the near three-year conflict over the last few weeks.

Russian President Vladimir Putin last week signed a decree lowering the threshold for the use of nuclear weapons, days before launching the nuclear-capable hypersonic Oreshnik missile at Ukraine. (AFP)