DONETSK, Ukraine — Ukraine pressed ahead on Sunday with its military assault to stamp out pro-Russian separatists in the east of the country with its most intensive artillery bombardment of this rebel capital yet.

The attack with artillery and ground-to-ground rockets defied Russian threats to intervene here as the civilian death toll rose.

It also reinforced the Ukrainian leadership’s rejection of a cease-fire on humanitarian grounds offered on Saturday by the head of the main pro-Russian separatist group here, the Donetsk People’s Republic. The separatist leadership clarified Sunday that the cease-fire offer had covered only so-called green routes, or roads used by evacuees.