BAKHMUT, Ukraine — With Luhansk Province firmly in Russia’s grasp after weeks of brutal fighting, the country’s military forces were already setting their sights on the next target. On the outskirts of Bakhmut, a key supply hub for Ukrainian forces, the Russian Army was ramping up its shelling as an apparent prelude for an inch-by-inch offensive into the province of Donetsk.
The tactic drove out Ukrainian defenders from the last two cities standing in Luhansk, the other province in the eastern Donbas region, whose capture President Vladimir V. Putin of Russia has described as a crucial objective of his war.
In Sloviansk, one of the cities in Donetsk that lies in Russia’s path, the mayor, Vadym Lyakh, urged residents on Tuesday to flee the city, which he said was now on the front lines. “Artillery is already hitting the city,” he warned in an interview on Ukrainian television, saying that 40 houses were destroyed by shelling the day before. In a Facebook post, he said that one person was killed on Tuesday and seven others wounded in an attack on the city’s central market.
Sloviansk and Bakhmut are likely to be the next cities to face the brunt of the Russian war machine, analysts say. To capture all of Donetsk, Russian forces would most likely need to take Kramatorsk, an administrative center and the headquarters of Ukrainian military forces in the east.
The speaker of the lower house of the Russian Parliament, Vyacheslav Volodin, called for Russian forces to continue their assault, accusing Ukraine without evidence of instigating the fighting.
“They themselves are doing everything to ensure that our troops do not stop at the borders of Luhansk and Donetsk people’s republics,” he said on Tuesday, using the names of the provinces favored by Russia-backed separatists.
Ukraine’s armed forces said Tuesday that Russian troops were focused on restoring transport infrastructure in Luhansk, which has been devastated by months of relentless bombardment, in apparent preparation for a push into Donetsk.
The current phase of Russia’s offensive has been marked by incremental gains backed by withering artillery fire, and Ukrainian forces have often withdrawn from the charred husks of bombed-out cities and towns rather than risk further casualties. It remains to be seen how heavily they will defend cities in Donetsk as they rack up hundreds of dead and wounded soldiers a day and are forced to rely on National Guard units and other less-well-trained fighters.
But Russian forces are also taking heavy losses, and Ukrainian military officials say that their goal is to draw out the fighting in the east as long as possible to exhaust their adversary and buy time until more Western weapons reach the front. In recent days, Ukrainian forces say they have destroyed Russian military infrastructure in occupied areas far from the front lines, a sign that newly arrived, longer-range artillery systems are being put to use.
On Tuesday, Ukraine said it had used one of the most advanced long-range weapons systems provided by the United States — a High Mobility Artillery Rocket System, or HIMARS — to strike Russian ammunition depots in Dibrivne, in the Kharkiv region of Ukraine. That was around 40 miles inside territory controlled by separatists loyal to Russia.
But any ability of Ukrainian troops in the field, many of whom have been under continuous shelling for weeks and even months, and have been taking heavy casualties, to follow up with counterattacks is in deep question.
Andrew E. Kramer and Maria Varenikova reported from Bakhmut, Ukraine, and Shashank Bengali and Matthew Mpoke Bigg from London.
