The cities of Severodonetsk and Lysychansk in Luhansk are increasingly under duress, according to the official, who spoke under condition of anonymity due to the sensitivity of the matter.
Meanwhile, Ukrainian officials said Russia is bombarding a chemical plant that has been sheltering hundreds of soldiers and civilians in Severodonetsk, which is a strategic city mostly under Russian control following weeks of intense battles.
According to Serhiy Haidai, governor of the Luhansk region, Russia is set to "throw all their reserves in order to capture the city" within a day or two so that it can take control of the Lysychansk-Bakhmut highway, which is a vital supply route.
Ukrainian officials also said they need more weapons to counter Russia's offensive. Vadym Skibitsky, who serves as the deputy head of Ukraine's military intelligence, said that Russia's artillery significantly surpasses that of Ukraine at a 10:1 or 15:1 ratio.
"Ukraine has one artillery piece to 10 to 15 Russian artillery pieces. Our western partners have given us about 10 percent of what they have," Skibitsky said. He also added that Ukraine's success at holding off the Russian forces will depend on whether or not it receives more weapons from western countries.
Meanwhile, local authorities in Western Ukraine said that 22 people were injured in a missile strike near Chortkiv on June 11, but Russia claimed that it targeted a warehouse containing missiles.
Bodies of dozens of fighters who died defending the Azovstal complex in Mariupol against months-long Russian attacks are still to be recovered, according to a former commander of the Azov Regiment that served as the backbone of defense in the area.
The commander, Maksym Zhorin, said nearly 220 bodies are now in Kyiv, but almost as many more bodies need to be recovered.
So far, the bodies that have already been recovered came from two exchanges with Russian forces, one resulted in 160 war deaths on each side, while the second ended with "almost 60 bodies," Zhorin said.
Talks are underway for body exchanges.
So far, Azov Regiment fighters made up about a third of the bodies recovered. Other fatalities were from other groups that defended the city, including the infantry, police and border guards. (Related: Ongoing Russia-Ukraine conflict pushing global economy closer to collapse.)
The estimates were based on the uniforms, according to Zhorin, although he said that it would take longer to identify the bodies individually.
He said: "Now the very difficult work, the very difficult process, of identifying the bodies is beginning. The thing is that most of these bodies are in a very awful state, and it is impossible to recognize them visually, for example."
The Azov Regiment is controversial for its far-right links, and was one of the key units that defended the Azovstal steel works for nearly three months against Russian attacks before they surrendered in May.
While the war with Ukraine is ongoing, Russians at home and abroad celebrated Russia Day on Sunday, June 12. The Russian Embassy in Britain said that Russia Day is "considered to be a holiday of liberty and civic peace."
Marking the day were protests held inside and outside of Russia as protesters laid a mourning wreath in front of the Russian Embassy in Kyiv and hung a banner on the gate that read: "The last day of Russia."
Antiwar artists in Moscow also placed a flag outside the headquarters of the Russian armed forces' General Staff, which said: "This is not our day."
The Russian state police was said to have detained about 50 citizens who allegedly planned to protest against their country's assault on Ukraine.
According to an independent Russian human rights media project, some Russians stood in certain parts of Moscow to protest their independence day, with police arresting political activists, journalists and citizens who attended the protests, accusing them of discrediting the actions of the Russian army.
These protests have been growing in Russia as the assault on Ukraine continues.
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This video is from the High Hopes channel on Brighteon.com.