Moscow on Saturday launched a "counter-terror operation" in three border regions adjoining Ukraine to halt Kyiv's biggest cross-border offensive in the two-and-a-half year conflict.

Ukrainian units stormed across the border into Russia's western Kursk region on Tuesday morning in a shock attack and have advanced several kilometres, according to independent analysts.

Russia has deployed additional troops and equipment, including tanks, rocket launchers and aviation units to stop the advancing troops.

Russia's national anti-terrorism committee said late Friday it was starting "counter-terror operations in the Belgorod, Bryansk and Kursk regions ... in order to ensure the safety of citizens and suppress the threat of terrorist acts being carried out by the enemy's sabotage groups."

Under Russian law, security forces and the military are given sweeping emergency powers during "counter-terror" operations.

Movement is restricted, vehicles can be seized, phone calls can be monitored, areas are declared no-go zones, checkpoints introduced, and security is beefed up at key infrastructure sites.

The anti-terrorism committee said Ukraine had mounted an "unprecedented attempt to destabilise the situation in a number of regions of our country."

It called Ukraine's incursion a "terrorist attack" and said Kyiv's troops had wounded civilians and destroyed residential buildings.

Ukrainian leaders have remained tight-lipped on the operation, and the United States, Kyiv's closest ally, said it was not informed of the plans in advance.

But President Volodymyr Zelensky has appeared to tout his troops early successes, saying earlier this week that Russia must "feel" the consequences of the full-scale offensive it has waged against Ukraine since February 2022.

Russia's defence ministry published footage on Saturday of tank crews firing on Ukrainian positions in the Kursk region, as well as an overnight air strike, after it said Friday it had deployed yet more units to the border region.

It also said it had downed 26 Ukrainian drones that tried to attack the region overnight.