Ukraine, on the brink of losing the eastern region of Luhansk to Russia, is warning that its outgunned military desperately needs faster Western arms deliveries.

Fierce street fighting is continuing in the strategic city of Severodonetsk, but "most of the city is controlled by Russians," the Luhansk governor said Saturday. An adviser to Ukraine's government said its forces could respond with only about one artillery round for every 10 fired by Russia.

Kyiv's European allies have vowed to step up military aid -- even as many appear hesitant about Ukraine's bid for European Union membership. European Commission President Ursula von der Leyen arrived in Kyiv on Saturday to discuss Ukraine's E.U. candidacy with President Volodymyr Zelensky ahead of an expected recommendation from the commission on Ukraine's status next week.

Meanwhile, President Joe Biden said Zelensky "didn't want to hear" U.S. warnings of a potential Russian attack before the invasion began, according to the Associated Press. Ukrainian officials have objected to Biden's claim.

It's a likely scenario that Russia could seize control of the entire Luhansk region of Ukraine within a few weeks, creating a new de facto front line in the war that could last for some time, a senior U.S. defense official said.

Such a move would leave Russia short of its war aims of capturing all of the Luhansk and Donetsk regions, but still amount to a partial win for Russian forces.

The Ukrainian cities of Severodonetsk and Lysychansk, in Luhansk, are increasingly under duress and could fall to Russian forces within a week, the official said, speaking on the condition of anonymity because of the sensitivity of the issue.

Russia's progress, however, remains incremental overall and is coming at great cost to its own forces in terms of deaths and injuries, the official said.

Ukrainian forces have been fighting a very effective "mobile area defense," in which Russia presses forward with its assault as Ukrainian forces fall back, only for Ukrainian forces to then rebound and take back land.

"The Ukrainians are doing a really good job here," the official said.

Casualties are likely mounting on both sides as Ukrainian and Russian forces engage in intense street fighting in Severodonetsk, the strategically important city in the Luhansk region, according to an intelligence update from Britain's Defense Ministry.

As of Friday, Russian troops have not been able to make advances in the city's south, but they are combining artillery firepower with airstrikes to overwhelm Ukrainian defenses, the ministry said.

In the past two months, the Russian military has launched dozens of heavy anti-ship missiles against land targets, the Defense Ministry added, noting that these weapons can cause "significant collateral damage and civilian casualties" because of their inaccuracy. It said the decision to deploy such inefficient weapons was probably due to Russia's shortage of more precise missiles, while Ukrainian air defenses are still deterring Russian airstrikes.

Roughly 10,000 Ukrainian soldiers have been killed since the Russian invasion began in late February, a military adviser to Zelensky said Saturday.

When asked by journalist Mark Feygyn if 10,000 Ukrainian soldiers have been killed, military adviser Oleksiy Arestovych responded, "Yes, something like that."

Zelensky adviser Mykhailo Podolyak said this week that between 100 and 200 Ukrainian soldiers are being killed every day.

Arestovych estimated to Feygyn that the daily numbers for Ukrainian casualties were more like "200 to 300 die, no less," but that the figures fluctuate.

The military adviser claimed that while roughly 10,000 Ukrainian soldiers have died, Russia's losses have been even greater. The Ukrainian government has said that more than 30,000 Russian troops have died, while British intelligence has estimated the number to be closer to 15,000. Russia has not given an update on the number of soldiers killed since late March.

The Washington Post could not immediately verify the figures referenced by Arestovych.

Zelensky said Saturday that it's "too late" to persuade Russia to end its invasion, saying it's up to the world to put Russia "in its place."

Speaking via video at the Shangri-La Dialogue, a key annual security summit in Singapore, Zelensky was stern in saying there was no more "gray area" when it came to supporting either Ukraine or Russia in the fourth month of the invasion.

"If you are now for peace, then you support Ukraine. If you support this particular war, then you find mutual understanding with the Russian Federation. That's all," he said, according to Interfax. "It's too late to discuss. It's a political game and nothing more."

He added, "I think that today the whole world must put the Russian leadership in its place. And their place is in their territory. And there they must live and decide what to do."

The Ukrainian president said the period in which his government tried to "calm down" Russian President Vladimir Putin and the Kremlin had come and gone, and that Ukraine must continue to put pressure on Russia.

"We respect international law, we respect the sovereignty and territorial integrity of each state," he said. "But please do not forget that the war is being fought on our territory. It is a war on our land."