KYIV, Ukraine • NATO estimated Wednesday that 7,000 to 15,000 Russian soldiers have been killed in four weeks of war in Ukraine, where fierce resistance from the country’s defenders has denied Moscow the lightning victory it sought.

By way of comparison, Russia lost about 15,000 troops over 10 years in Afghanistan.

A NATO military official said the alliance’s estimate was based on information from Ukrainian authorities, what Russia has released — intentionally or not — and intelligence gathered from open sources. The official spoke on condition of anonymity under ground rules set by NATO.

Ukraine has released little information about its own military losses, and the West has not given an estimate, but President Volodymr Zelensky said nearly two weeks ago that about 1,300 Ukrainian servicemen had been killed.

When Russia unleashed its invasion Feb. 24 in Europe’s biggest offensive since World War II, a swift toppling of Ukraine’s government seemed likely. But with Wednesday marking four full weeks of fighting, Moscow is bogged down in a grinding military campaign.

With its ground forces slowed or stopped by hit-and-run Ukrainian units armed with Western-supplied weapons, Russian President Vladimir Putin’s troops are bombarding targets from afar, falling back on the tactics they used in reducing cities to rubble in Syria and Chechnya.

In an ominous sign that Moscow might consider using nuclear weapons, a senior Russian official said the country’s nuclear arsenal would help deter the West from intervening in Ukraine.

“The Russian Federation is capable of physically destroying any aggressor or any aggressor group within minutes at any distance,” Dmitry Rogozin, the head of the state aerospace corporation, Roscosmos, said in televised remarks. He noted that Moscow’s nuclear stockpiles include tactical nuclear weapons, designed for use on battlefields, along with far more powerful nuclear-tipped intercontinental ballistic missiles. Roscosmos oversees missile-building facilities.

U.S. officials long have warned that Russia’s military doctrine envisages an “escalate to deescalate” option of using battlefield nuclear weapons to force the enemy to back down in a situation when Russian forces face imminent defeat. Moscow has denied having such plans.

Rogozin is known for his bluster, and he did not make clear what actions by the West would be seen as meddling, but his comments almost certainly reflect thinking inside the Kremlin. Putin has warned the West that an attempt to introduce a no-fly zone over Ukraine would draw it into a conflict with Russia. Western nations have said they would not create a no-fly zone to protect Ukraine.

As President Joe Biden left for Europe to meet with key allies about new sanctions against Moscow and more military aid to Ukraine, he warned there is a “real threat” Russia could use chemical weapons.

On the eve of a meeting with Biden, European Union nations signed off on another 500 million euros ($550 million) in military aid for Ukraine.

The U.S. has also determined that Russian troops have committed war crimes in Ukraine, and it will work to prosecute the offenders, Secretary of State Antony Blinken said. He cited evidence of indiscriminate or deliberate attacks against civilians and the destruction of apartment buildings, schools, hospitals, shopping centers and other sites.

Addressing Japan’s parliament, Zelensky said thousands of his people have been killed, including at least 121 children.

“Our people cannot even adequately bury their murdered relatives, friends and neighbors. They have to be buried right in the yards of destroyed buildings, next to the roads,” he said.

Still, major Russian objectives remain unfulfilled. The capital, Kyiv, has been bombarded repeatedly but is not even encircled.

Near-constant shelling and gunfire shook the city Wednesday, with air raid sirens wailing and plumes of black smoke rising from the western outskirts, where the two sides battled for control of multiple suburbs.

Mayor Vitali Klitschko said at least 264 civilians have been killed in the capital since the war broke out.

Zelensky said 100,000 civilians remain in the city, which had 430,000 people before the war.

Efforts to get desperately needed food and other supplies to those trapped have often failed.

A serviceman carries the photo of Capt. Andrei Paliy, a deputy commander of Russia’s Black Sea Fleet, during a farewell ceremony Wednesday in Sevastopol, Crimea.

the associated press