Russian soldiers carried out a full-scale attack to encircle Ukrainian troops in twin cities straddling a river in eastern Ukraine, a struggle that might determine the success or failure of Moscow's primary campaign in the east.

Three months to the day after Russia invaded Ukraine, officials in the second-largest city of Kharkiv were set to open the subterranean metro, where thousands of citizens had sought refuge from months of continuous bombing.

The reopening is a symbol of Ukraine's largest military victory in recent weeks: driving Russian forces largely out of artillery range of Kharkiv, like they did in March from the capital city of Kyiv.

However, the major battles of the latest phase of the war are still going farther south, where Moscow is aiming to conquer the Donbas region comprising two eastern provinces, Donetsk and Luhansk, and trap Ukrainian forces in a pocket along the main eastern front.

The easternmost portion of the Ukrainian-held Donbas pocket, the city of Sievierodonetsk on the east bank of the Siverskiy Donets river, and its twin city Lysychansk on the west bank have become the critical battlefield there, as Russian forces advance from three directions to encircle them.

"The enemy has concentrated its efforts on launching an offensive to encircle Lysychansk and Sievierodonetsk," said Serhiy Gaidai, the governor of Luhansk, where the two cities are among the last remaining Ukrainian territory.

Monday, Reuters journalists in the Donbas, who had reached Bakhmut further to the west, witnessed and heard severe bombardment on the highway leading to Lysychansk. Along with troop-carrying buses, Ukrainian armored vehicles, tanks, and rocket launchers were advancing towards the front lines.

In Slovyansk, one of the largest Donbas cities still under Ukrainian control, air raid sirens wailed on Tuesday morning, but the city's streets remained lively, with a crowded market, youngsters riding bicycles, and a street musician playing violin near a store.

Two empty public transportation buses were going towards the frontline town of Lyman, escorted by a police car and a military vehicle, to rescue inhabitants from severe bombardment there.

Gaidai reported that Ukrainian forces have expelled the Russians from Toshkivka, a settlement located just south of Sievierodonetsk. A residence in Sievierodonetsk was shelled overnight, resulting in the death of four persons.

The battle follows the surrender of Ukraine's military in the port of Mariupol last week after nearly three months of siege, during which Kiev estimates that tens of thousands of people perished.