Russia ratcheted up its battle for control of Ukraine’s eastern industrial heartland on Tuesday, intensifying assaults on cities and towns along a front hundreds of miles long in what officials on both sides described as a new phase of the war.

After a Russian push to overrun the capital failed, the Kremlin declared that its main goal was the capture of the eastern Donbas region, where Moscow-backed separatists have been fighting Ukrainian forces for eight years.

If successful, that offensive would give President Vladimir Putin a vital piece of Ukraine and a badly needed victory in the now 7-week-old war that he could present to the Russian people amid mounting casualties and economic hardship caused by the West’s sanctions.