Russia has lost more than 10% of forces it sent into Ukraine, a senior Pentagon official said Tuesday.

The official, who spoke to reporters on condition of anonymity, said Moscow now has "slightly below" 90% of the forces it amassed in Belarus and western Russia ahead of its military operation that began Feb. 24.

The US estimate comes after a pro-Kremlin tabloid reported Monday what it said was Russian Defense Ministry data indicating 9,861 Russians have been killed and 16,153 injured during the Russian war on Ukraine. The report from Komsomolskaya Pravda was quickly taken down.

The Russian Defense Ministry has not publicly identified the number of casualties that Russia has sustained since early March when it said 498 soldiers had died. Ukraine has claimed to have killed 15,000 Russian troops, including five generals.

The US official said the Biden administration is continuing to see signs that Russia is facing logistical problems, including difficulties in transporting fuel, food and supplies to troops in Ukraine, in part because of Ukrainian resistance.

The shortages have become so acute that some Russian soldiers contracting frostbite due to a lack of appropriate gear, the official said.

- Some troops have actually suffered, and been taken out of the fight because of frostbite. They are having continued logistics and sustainment issues, and again because the Ukrainians had done a good job frustrating their efforts to resupply as well as because we don't think they properly planned for logistics and sustainment on the level that they needed to -  said the official.

The official also said that the US is seeing indications that Ukrainians "are now able and willing to take back territory that the Russians have taken again".

According to UN estimates, at least 953 civilians have been killed and around 1,557 others injured in Ukraine since Russia began its attack on its western neighbor.

However, the UN has warned that the true toll is likely to be much higher because it has not been able to gain access to areas of heightened hostility.

The war has also driven 10 million people from their homes, either internally or as refugees who fled abroad, according to the UN refugee agency.