The administrative center of the Luhansk region, Severodonetsk, has been subjected to unrelenting Russian bombing.
Ukrainian forces engaged the Russians in house-to-house combat before retiring to a massive chemical plant on the city's outskirts, where they hid in its vast underground facilities.
To encircle Ukrainian forces, Russian forces have gained gains around Severodonetsk and the nearby city of Lysychansk, on a steep bank across the river.
To avert this, according to Serhiy Haidai, governor of Luhansk, the Ukrainian army has been ordered to withdraw from Severodonetsk.
"We will need to pull our troops back," he said.
"Staying at the destroyed positions makes no sense, as the number of casualties in poorly fortified areas will increase daily."
Mr. Haidai stated that the Ukrainian soldiers "received the order to retreat to new positions and continue fighting there," but he did not provide any additional information.
He stated that the Russians were also pushing against Lysychansk from Zolote and Toshkivka and that Russian reconnaissance units had made incursions into the city's outskirts but were repelled by its defenders.
Following a failed attempt to capture Kyiv, the capital of Ukraine, in the early stages of the February 24 invasion, Russian forces have moved their attention to the Donbas area, where Ukrainian troops have been fighting Moscow-backed separatists since 2014.
The Russian military controls around 95% of Luhansk province and approximately 50% of adjacent Donetsk province, the two provinces that comprise the Donbas.
After repeated pleas to its western partners for heavier armament to confront Russia's superior firepower, the Ukrainian defense minister said that American medium-range rocket launchers had arrived in response.
On Wednesday, a US defense official verified that all four of the promised High Mobility Artillery Rocket Systems (HIMARS) had been delivered to Ukrainian forces but stated that it was unclear whether or not they had been deployed.
The United States approved the delivery of precision-guided systems to Ukraine at the end of May. Once the weapons arrived in the region, Ukraine's military required approximately three weeks of training to operate them.
Rockets can travel around 45 miles.