Russia's military said Tuesday that Ukraine fired US-supplied long-range missiles at a military facility in the Bryansk border region, in what would be the first attack since Washington authorised the use of its weapons.

"At 03:25 am, the enemy struck a site in the Bryansk region with six ballistic missiles. According to confirmed data, US-made ATACMS tactical missiles were used," the defence ministry said in a statement.

Ukraine had for months been demanding that Washington let it use the longer-range ATACMS missiles to hit sites on Russian territory.

Moscow has said the use of Western weapons to attack Russia's internationally recognised territory would make the United States a direct participant in the conflict and pledged an "appropriate and palpable response".

In its statement, Russia's defence ministry said five missiles were shot down by its air defences, while fragments from a sixth fell onto an unspecified "military facility", causing a small fire.

"There were no casualties or damage," it said. 

Ukraine's foreign minister hailed on Monday the permission to use the missiles for strikes inside Russia as a potential "game changer" in the nearly three-year-old conflict.