In the cities of Berdyansk and Luhansk, an air defense system, other machinery, and a weapons dump were reportedly hit, according to a statement from the special forces.
The action also resulted in the deaths or injuries of dozens of Russian soldiers.
Neither an independent confirmation of the attack nor a statement from the Russian military have been made.
The air defense systems "effectively intercepted hostile missiles" above Berdyansk, according to Vladimir Rogov, the Russian-appointed governor of the province of Zaporizhzhia that is under occupation. Rogov said that information regarding injuries and damage was being examined and would be released later.
Unverified footage on a pro-Russian social media account, however, claims to show explosions and rockets flying while a voiceover reports that an ammo dump has been hit. The video is reported to have been shot in Berdyansk.
Another Russian blogger detailed how US-made ATACMS rockets were used in a strike on an airstrip, dealing what the author called a "severe blow" and damaging both persons and technology.
The attack on Berdyansk took place at 4:00 local time (01:00 GMT), according to the Ukrainian military, then on Luhansk at 11:00 local time.
The distance between Berdyansk and the closest front line is about 85 km (53 miles), but Luhansk is about 100 km away.
There have been reports of clashes along the front line, particularly near the Ukrainian-held towns of Avdiivka, Kupyansk, and Lyman, which have recently been subjected to severe Russian artillery fire.
Two persons are reportedly trapped in the wreckage of a dormitory building that was demolished in a Russian attack on the eastern city of Slovyansk, according to the emergency services of Ukraine.
Authorities in Odesa said that while debris from downed Russian drones damaged a yacht club and several yachts, no injuries were reported.
Through a significant counteroffensive, Ukraine has been attempting to retake territory that Russia has taken over in the east and south of the nation, but success has been sluggish so far.
In an effort to hinder Moscow's military operations, it has also frequently attacked Russian sites from the air.
Along with attacking Ukrainian forces in the east around Avdiivka and Kupyansk, Russia has recently sustained significant fatalities, according to Ukrainian accounts.