Russian forces have declared victory in the eastern Ukrainian region of Luhansk. They are now shifting their focus to the neighboring region of Donetsk.
Analysts at the Institute for the Study of War in Washington say Russian leaders may push for even more territory.
Residents of Slovyansk fear their hometown could become the next target in the offensive. Pro-Russian fighters occupied the city eight years ago.
Ukrainian commanders are determined to quell those ambitions. They are using rocket systems from the US to strike targets far away.
However, Russian defense officials claim they have managed to destroy some of those weapons.
Defence Ministry spokesperson Igor Konashenkov said the Russian Armed Forces have destroyed two US-made HIMARS rocket systems and two ammunition depots. He said the forces continue to strike military facilities in Ukraine.
Ukrainian officials have dismissed those claims as false.