Russian forces have further intensified their shelling of the last Ukrainian strongholds in the eastern Luhansk region, making their biggest gains in weeks and closing in on capturing the key cities of Syeveyerodonetsk and Lysychansk.

In the face of Russia's all-out assault on the Donbas, President Volodymyr Zelenskiy said on May 27 that he must hold talks with Russian President Vladimir Putin in order to safeguard Ukraine's sovereignty and existence.

Serhiy Hayday, the governor of the Luhansk region, said that Ukrainian forces were engaged in a "fierce defense" of Syevyerodonetsk, which is two-thirds surrounded by Russian forces.

"Very strong" shelling has destroyed 90 percent of the housing in the city, Hayday added, also citing information he received from the city's mayor, Oleksandr Stryuk.

Stryuk said earlier that at least 1,500 people have been killed in his city since the start of Russia's invasion in late February. About 12,000 to 13,000 remain in the city -- down from a pre-war population of about 100,000, he said.

Moscow-backed separatists on May 27 also claimed full control of the important battlefield town of Lyman, some 60 kilometers west of Syevyerodonetsk, but the Ukrainian Defense Ministry denied that the major railway hub had fallen, saying in a statement that its forces continue to counteract Russian attempts to overrun it.

Lyman has been a front-line target as Russian forces press down from the north, one of three directions from which they have been attacking Ukraine's industrial Donbas region.

In its daily intelligence bulletin, Britain's Ministry of Defense said that, while Russian ground forces continue to put pressure on the Syeyverodonetsk pocket with some success,Moscow appears to have moved 50-year-old T-62 tanks in recent days from deep storage into the theater of operations in the Donbas.

The report assessed that the move proves Russia's shortage of modern, combat-ready equipment. Furthermore, "the T-62s will almost certainly be particularly vulnerable to anti-tank weapons and their presence on the battlefield," British intelligence said.

Zelenskiy, in an address on May 27 to an Indonesian think tank, said talking to Putin will likely be necessary to end the war.

"What do we want from this meeting?... We want our lives back... We want to reclaim the life of a sovereign country within its own territory," he said, adding that Russia did not appear to be ready yet for serious peace talks.

In response, the Kremlin on May 27 accused Kyiv of a lack of clarity.

"The Ukrainian leadership constantly makes contradictory statements. This does not allow us to fully understand what the Ukrainian side wants," Kremlin spokesman Dmitry Peskov said in a call with reporters.

Zelenskiy also accused Russia -- which has said that it would allow Ukraine to resume its grain exports by sea if the West lifts some sanctions imposed on it for starting the war -- of weaponizing the global food supply crisis.

Zelenskiy has become increasingly critical of the West in recent days as the European Union moves slowly toward a possible Russian oil embargo while Ukraine's military situation becomes increasingly difficult in the east.

The embargo requires unanimity among the bloc's 27 members, but Hungary opposes the move, arguing that its economy would be gravely hit.

Zelenskiy blasted the lack of agreement within the EU. "How many more weeks will the European Union try to agree on a sixth package?" he asked.

In Geneva, the UN rights office (OHCHR) said in a statement on May 27 that more than 4,000 civilians have been killed in Ukraine since Russia's invasion began on February 24, although the true number is likely much higher.

In total, 4,031 people have been killed, including nearly 200 children, according to the OHCHR, which has dozens of monitors in the country. Most were killed by explosive weapons with a wide impact such as shelling from heavy artillery or air strikes.

Russia has denied targeting civilians in the conflict.

Also on May 27, the United Nations refugee agency (UNHCR) said that more than 6.6 million Ukrainian refugees have fled to neighboring countries, and 2.9 million have moved on to other European nations.

"According to the latest data we have available... 2.9 million refugees have moved beyond countries neighboring Ukraine," UNHCR spokeswoman Shabia Mantoo told a briefing in Geneva.

The UNHCR said the largest numbers of Ukrainian refugees in non-neighboring countries were in Germany, the Czech Republic, and Italy.

"They often arrive in a state of distress and anxiety, having left family members behind, without a clear plan for where to go, and with less economic resources and connections than those who fled earlier."

Before the February 24 invasion, Ukraine had a population of 37 million in the regions under Kyiv's control, excluding Russia-annexed Crimea and the pro-Russian separatist-controlled regions in the east.

With reporting by Reuters, AP, AFP, CNN, and BBC