Videos circulating online show intense fighting taking place in Ukraine's besieged port city of Mariupol.

The footage, verified by ABC News, was taken by a Russian state media journalist who is embedded with the Russian military. The videos were posted online Thursday, though the exact date of filming was unknown. Based on the location of the fighting, ABC News assesses it is highly likely the videos were shot in the past couple of days.

One video shows a Russian tank firing multiple times on the streets of Mariupol. Another video shows the Russian journalist filming himself in Mariupol as tanks open fire and gunshots erupt all around him.

The strategic port city in southeastern Ukraine has been under heavy Russian bombardment for weeks and tens of thousands of civilians remain trapped there.

-ABC News' Fergal Gallagher

Despite Russia's claims of curbing its military activity around Chernihiv, "significant Russian shelling and missile strikes have continued" in the besieged northern Ukrainian city, the U.K. Ministry of Defense said Thursday in an intelligence update.

Meanwhile, Russian forces continue to hold positions to the east and west of Ukraine's capital, Kyiv, "despite the withdrawal of a limited number of units," according to the ministry.

"Heavy fighting will likely take place in the suburbs of the city in the coming days," the ministry added.

Heavy fighting also continues in Ukraine's southern port city of Mariupol, "a key objective of Russian forces," according to the ministry.

"However Ukrainian forces remain in control of the center of the city," the ministry said.

The Russian government is "concerned" by recent statements from U.S. officials claiming that Russian President Vladimir Putin "felt misled" by his advisers and the Russian military on the war in Ukraine, Kremlin spokesman Dmitry Peskov said at a press conference Thursday.

"We do not just regret this. This is a source of our concern," Peskov told reporters, "because such an utter lack of understanding is the reason why erroneous, rash decisions are made with very bad consequences."

"It looks like neither the [U.S.] Department of State nor the Pentagon know what is really happening in the Kremlin," he added. "They simply do not understand what is going on in the Kremlin. They do not understand President Putin. They do not understand the decision-making mechanism. They do not understand our work style."

Russia has announced a localized cease-fire in Ukraine's besieged southern port city of Mariupol on Thursday to allow civilians to be evacuated.

A humanitarian corridor from Mariupol to Zaporizhzhia, via the Russian-controlled port of Berdiansk, would be opened from 10 a.m. local time, according to the Russian Ministry of Defense.

"For this humanitarian operation to succeed, we propose to carry it out with the direct participation of the U.N. High Commissioner for Refugees and the International Committee of the Red Cross," the Russian defense ministry said in a statement Wednesday night.

Ukrainian Deputy Prime Minister Iryna Vereshchuk said in a later statement via Telegram that the Red Cross confirmed Russia had agreed to open a humanitarian corridor to Mauripol, where tens of thousands of civilians remain trapped with no electricity and dwindling supplies after weeks of Russian bombardment. A convoy of 45 evacuation buses was headed to the city to collect civilians, according to Vereshchuk.

A number of previous attempts to establish humanitarian corridors out of Mariupol have failed, with Russia and Ukraine trading accusations of breaking cease-fires and sabotaging evacuation efforts.

-ABC News' Julia Drozd

All Russian troops have left the Ukrainian cities of Kyiv and Chernihiv, withdrawing north toward the borders of Belarus and Russia to consolidate before likely redeploying to the Donbas region in eastern Ukraine, a senior U.S. defense official told reporters Wednesday.

But even with the Russians gone, the territory remains treacherous.

"There are some indications that they left behind mines and things like that, so the Ukrainians are being somewhat careful in some areas north of Kyiv as they begin to clear the ground and clear the territory and re-occupy it," the official said.

While the U.S. hasn't yet seen these troops redeploy elsewhere in Ukraine, it'll likely happen soon, according to the official. Ukrainian forces are preparing for a major fight in Donbas, the official said.

The official also said the Pentagon is "monitoring" an apparent nitric acid explosion in Ukraine's Luhansk region, which Russia blamed on Ukraine.

"We've seen the Russians claim that this was a Ukrainian attack on this. We do not believe that is true," the official said. "We do believe that the Russians are responsible, but exactly what they used when they did it, why they did it, what the damage is, we just don't have that level of detail," the official said.

The official also noted that a small number of Ukrainians currently in the U.S. for "professional military education" were pulled aside for a couple days of training on Switchblade drones, which the U.S. is sending overseas as part of its military aid, according to the official.

"Although it's not a very difficult system to operate, we took advantage of having them in the country to give them some rudimentary training on that," the official said.

-ABC News' Matt Seyler