WASHINGTON - The United States believes that Russia's military is taking hundreds of casualties a day in its war in Ukraine, including having lost thousands of lieutenants and captains in total, a senior U.S. defense official said on Friday.

Nearly five months since President Vladimir Putin ordered an invasion of Russia's neighbor, its forces are grinding through the Donbas region of eastern Ukraine and occupy around a fifth of the country.

The United States estimates that Russian casualties in Ukraine so far have reached around 15,000 killed and perhaps 45,000 wounded, CIA Director William Burns said on Wednesday, adding that Ukraine has also endured significant casualties.

The official, speaking on the condition of anonymity, said that in addition to the lieutenants and captains killed, hundreds of colonels and "many" Russian generals had been killed as well.

"The chain of command is still struggling," the official said.

Russia classifies military deaths as state secrets even in times of peace and has not updated its official casualty figures frequently during the war. On March 25 it said 1,351 Russian soldiers had been killed.

The Kyiv government said in June that 100 to 200 Ukrainian troops were being killed per day.

The United States also believed that Ukraine had destroyed more than 100 "high-value" Russian targets inside Ukraine, including command posts, ammunition depots and air-defense sites, the U.S. official said.

The United States has provided $8 billion in security assistance since the war began, including $2.2 billion in the last month.

Earlier this week, the Pentagon said it would provide Ukraine with four additional high mobility artillery rocket systems (HIMARS) in the latest weapons package.

Russia says it is waging a "special operation" to demilitarise its neighbour and rid it of dangerous nationalists.

Kyiv and the West say Russia is mounting an imperialist campaign to reconquer a pro-Western neighbour that broke free of Moscow's rule when the Soviet Union collapsed in 1991.

(Reporting by Idrees Ali; editing by John Stonestreet and Nick Macfie)