• Russian advances on Kyiv have slowed, but the Pentagon estimates Russian forces are roughly 25 kilometers (16 miles) outside Ukraine's capital.
• The most recent assessment made public by the U.K. Ministry of Defence said that Ukraine still controls Kharkiv and Chernihiv, both scenes of brutal fighting.
• The Ukrainians still "have significant air and missile defense capabilities," a U.S. Defense official said.

The Kremlin still wants its invasion troops to capture Kyiv, even as Russian forces continue running into stiff Ukrainian resistance, according to a Pentagon assessment shared with CNBC.

"We have every indication that they still want to take Kyiv, that they are advancing on the ground and trying to get closer," a senior Defense official said, speaking on condition of anonymity in order to share new details from the assessment.

Russian advances on the Ukrainian capital have slowed, but forces are roughly 25 kilometers (16 miles) outside the city, the person said. The official cautioned that distance is an estimate, and the movements on the ground are changing.

"We expect that they're going to want to continue to move forward and try to encircle the city [Kyiv] in the coming days," the official said. "They are not there yet, that's not happening yet, but that appears to be what they're interested in doing."

The most recent assessment made public by the U.K. Ministry of Defence said that Ukraine still controls not just Kyiv but also Kharkiv and Chernihiv, both scenes of brutal fighting for days.

"Despite continued attempts to suppress details of the conflict from the Russian population, the Russian Armed Forces has for the first time been forced to acknowledge suffering casualties," the U.K. ministry said.

On Monday, Ukraine's Ministry of Foreign Affairs claimed that Russian invasion forces had so far lost 4,500 personnel, almost 200 tanks and almost 60 aircraft, half of them helicopters.

CNBC is unable to independently confirm Ukraine's claims.

Ukraine air power, communications

The U.S. Defense official explained that the Russians began targeting Ukrainian missile defense capabilities early on, but "on day five, the Ukrainians have significant air and missile defense capabilities."

Ukraine's command and control are still intact as well, the official said. Aside from intermittent outages, communications are still available.

Command and control refers to Ukraine's ability to centrally coordinate its forces around the country, primarily through electronic means.

The official added that Russian forces will likely continue to target Ukraine's air and missile capabilities.

The United States, European Union and individual EU member states have promised more shipments of weaponry to Ukraine including anti-aircraft missiles and anti-tank missiles.

The Wall Street Journal reported on Monday that EU member countries were in negotiations to give fighter jets to Ukraine — particularly Soviet-built planes, which Ukrainian pilots know how to fly.

Missile attacks, logistics problems

The U.S. Defense official said that so far Russia has launched more than 380 missiles. When pressed further on Russian firepower, the official said "they're throwing a lot at the problem."

"They're launching missiles, medium-range, short-range, cruise missiles," the official added. "They're using artillery, they're using rockets, manned aircraft, they've got infantry there."

American and British officials continue to say that Russian units are dealing with supply disruptions and logistical failures.

The U.S. official said the Pentagon has seen no indication troops from Belarus are operating in Ukraine, despite external reports to the contrary. Belarus is closely aligned with Russia.

"Our best information is that the forces inside Ukraine are all Russians," the official said.

Nearly 75% of Russian forces staged along Ukraine's borders before the invasion have now crossed into the country, the U.S. Defense official said.