The Russian military's first month of war in Ukraine is coming to a close, and it couldn't have gone much worse from the Kremlin's perspective.

Russia anticipated easily getting to and overtaking the capital, Kyiv. Yet after four weeks, Russian forces have conquered few key cities and are facing significant and multiple self-inflicted problems while resorting to a military philosophy of terrorizing civilians into submission. Their struggles are in large part due to the strength of the Ukrainian resistance forces, who have in some places begun retaking areas Russians had once conquered.

"The Russians have not achieved any of the strategic objectives that they set out to and they certainly haven't achieved the objectives that they have, easily or without, without loss," Pentagon spokesman John Kirby said Tuesday. Russian forces “only have two population centers that they have actually taken” through the first four weeks of the war, he stated during a television appearance earlier that day, which amounts to a significant shortcoming from past expectations.

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Russia's failures have left the Pentagon unsure of what their "endgame is now," he added.

The Pentagon has claimed to have seen indications that Russian forces have faced logistical and sustainment problems, and Kirby reaffirmed it Tuesday.

“We continue to see indications that the Russians did not properly plan for logistics and sustainment. We know that they continue to have fuel issues across their force and that they're still struggling with food," he said. "So they're still having trouble feeding some of their troops. They either didn't properly plan for logistics or sustainment, or they didn't properly execute their plan, but they are still having problems."

A senior U.S. defense official told reporters last week that the department was seeing “anecdotal indications” that Russian forces’ morale is "flagging." It is “a function of poor leadership,” as well as a “lack of information that the troops are getting about their mission and objectives," the official said, adding, “I think disillusionment from being resisted as fiercely as they have been” has also contributed to the situation.

In addition to those problems, other soldiers have been "taken out of the fight because of frostbite," the official told reporters Tuesday. “They lack the appropriate cold-weather gear for the environment that they’re in."

The problems of poor equipment and a lack of supplies demonstrate Russia's faulty planning ahead of the invasion.

Ukrainian leaders have also claimed to have killed a number of top Russian commanders, though that hasn't been independently verified. Mykhailo Podoliak, a top adviser to Ukrainian President Volodymyr Zelensky, said Sunday that six Russian generals and dozens of colonels and other officers had been killed in Ukraine.

Among their total force in Ukraine (roughly 170,000), Ukrainian officials have said more than 15,000 have been killed in action, whereas a pro-Kremlin tabloid, owned by a Russian oligarch, published and then deleted a report citing Russia’s Defense Ministry saying that it was approaching 10,000 deaths days ago.

Russian leaders in Ukraine have been forced to communicate on unsecured phones and radios. Ukrainians were able to intercept a general’s call in one case, geolocate him, and launch an attack that killed him and his staff, according to the New York Times. Additionally, it's unclear to U.S. officials who, if anyone, is leading the entire operation in Ukraine, according to CNN, who also reported that units from different Russian military battalions in different parts of the country seem to be competing for resources instead of sharing and coordinating them.

In Russia, some leaders are acknowledging the setbacks, while others claim the situation in Ukraine is going according to plan.

Viktor Zolotov, the chief of Russia's national guard and a member of Putin's security council, said, “Not everything is going as fast as we would like,” at a church service led by Russian Orthodox Patriarch Kirill about a week and a half ago, whereas Dmitry Peskov, the chief spokesman for Russian President Vladimir Putin, said in a CNN interview Tuesday that, when asked if they had met any of its strategic objectives, “Not yet,” though he added, “It is going on strictly in accordance with the plans and with purposes that were established beforehand.”

Putin’s climate envoy, Anatoly Chubais, also stepped down from his role and left the country over his opposition to the invasion, Bloomberg News reported Wednesday.

With little to show for it, Russia has been able to bombard various Ukrainian cities, turning them into empty shells of themselves with mass graves, bombed-out buildings, and collapsed structures. Russia has resorted to attacking civilian targets in the more recent parts of the war.

"We have seen clear evidence that over the — certainly, over the last week or so, the Russians have deliberately and intentionally targeted civilian infrastructure, hospitals, places of shelter, and we also have indications of behavior on the ground by Russian forces that would likewise constitute war crimes. I'm not going to get into a list of it," the official added Tuesday, a day after Kirby said U.S. officials had seen "clear evidence" that Russian forces had committed war crimes.

Ukraine’s ambassador to the United States, Oksana Markarova, accused the Russian military of committing “genocide" during a panel conversation hosted by the U.S. Institute of Peace on Tuesday, arguing its tactics show “no military objective.”

The residents of the port city of Mariupol, which is strategically located between Crimea, which the Russians invaded back in 2014, and the Donbas territory, where fighting between pro-Russian separatists and Ukrainians has occurred for years, have faced some of the most barbaric acts of war.

Russian forces shelled a Mariupol maternity hospital, killing five people and injuring 17, and they bombed a theater there that had been serving as a shelter, even though Ukrainians had spelled out the word "children" in Russian in the front and back of the facility. Russian troops also bombed a school housing hundreds of people.

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Peskov did not rule out Russia's use of a nuclear weapon should it face "an existential threat for our country," while the White House has also warned about the possibility of a chemical attack.

The Russian military doctrine, known to the West as “escalate to de-escalate,” is based on the belief that Russia could use a small nuclear device to devastate an enemy without triggering a retaliatory strike because opposing nuclear forces would be concerned about escalating the situation to a full-blown nuclear war. NATO has warned about the possibility as well.

“I think it’s a real threat,” President Joe Biden said of a possible chemical attack on Wednesday morning. Days earlier, he called Putin a "war criminal."

The United Nations said that more than 950 Ukrainian civilians have been killed and more than 1,500 injured, though it warns that the total figures are most likely “considerably higher” due to the difficulty of calculating casualties in a war zone.