Mariupol has not yet fallen, despite Russia's demands that Ukrainian troops defending the besieged Ukrainian port city surrender, according to Ukrainian Prime Minister Denys Shmyhal.

"There [are] still our military forces, our soldiers, so they will fight until the end," Shmyhal told ABC News' George Stephanopoulos in an exclusive interview Sunday on "This Week."

Mariupol is a strategic city for Moscow because it would allow Russian forces in the south to connect with troops in eastern Ukraine's contested Donbas region. It would also give Moscow a key port.

Although Mariupol remains under the Ukrainian government's control, Shmyhal said the city's residents are suffering.

"They have no water, no food, no heat, no electricity," he said. "They ask all of our partners to support and help stop this humanitarian catastrophe."

-ABC News' Monica Dunn

Russian commanders in Mariupol "will be concerned by the time it is taking to subdue" the Ukrainian port city, the U.K. Ministry of Defense said Monday in an intelligence update.

"Concerted Ukrainian resistance has severely tested Russian forces and diverted men and materiel, slowing Russia's advance elsewhere," the ministry said.

Mariupol, a strategic port in eastern Ukraine's Donetsk Oblast, has been under heavy Russian bombardment since the start of the invasion on Feb. 24. Strong resistance from Ukrainian troops has prevented Russian forces from taking full control of the city.

Despite Russia's claims that it would not strike Ukrainian cities or threaten civilian lives, "the targeting of populated areas within Mariupol aligns with Russia's approach to Chechnya in 1999 and Syria in 2016," according to the ministry.

"The effort to capture Mariupol has come at significant cost to its residents," the ministry added. "Large areas of infrastructure have been destroyed whilst the population has suffered significant casualties."

The mayor of Kharkiv, Igor Terekhov, lashed out at Russia for continuing its onslaught on the city despite it being Orthodox Palm Sunday.

"Dear Kharkiv citizens, today is the 53rd day of war, the war in which we are defending our lives and honor fighting against the ruthless army of the aggressor," Terekhov said in a recorded address translated from Russian by The Associated Press.

"And also today is a big Orthodox holiday, Palm Sunday. But it looks like those who wear the letter Z do not have a cross on them," he added, referring to the omnipresent letter painted on Russian tanks.

Kharkiv, Ukraine's second-largest city and a key outpost in the country's east, has been under intense shelling for days. Several people were killed in attacks on Sunday.

"Even days that are sacred to Christians are no reason for the enemy to lessen bombardments on Kharkiv," Terekhov said.

The vast majority of people in both Russia and Ukraine are Orthodox Christians. Holy Week began on Sunday with Easter coming on April 24. Many in Ukraine, including Kharkiv, celebrated Palm Sunday in bomb-damaged churches or buildings without electricity.

"I congratulate you all, my fellow Kharkiv citizens, with Palm Sunday, and on the eve of the Holy Week, I want to wish fortitude to all of us," Terekhov said. "The enemy is testing our resolve, let us show them that Kharkiv citizens will not be broken or intimidated."

Multiple rockets struck the center of Ukraine's second-largest city on Sunday, killing at least five people and injuring 13, Ukrainian officials said.

Kharkiv, in northeast Ukraine, has been targeted by Russian shelling since the early days of the invasion, and Sunday was no exception. The barrage of rockets hit apartment buildings and left broken glass, debris and the part of at least one rocket scattered on the streets of Kharkiv, according to Ukrainian regional officials.

Firefighters and residents scrambled to douse flames in several apartments that caught fire.

A kindergarten school in the city was also damaged in the attack.

"There were four shells, one of them fell between the fence and the kindergarten. It turned everything upside down," a staff member at the school told reporters.

It was the second consecutive day of heavy shelling in the center of Kharkiv. The city's mayor, Ihor Terekhov, said three people were killed and 34 others were wounded by Russian missile strikes on Saturday.

One missile hit a community kitchen set up in Kharkiv by World Central Kitchen, a nonprofit organization run by celebrity chef Jose Andres. Four World Central Kitchen staff members were injured in the attack. Andres posted a message on Twitter reporting the staff members suffered non-life-threatening injuries and are going to be fine.

Jalina Porter, the State Department's deputy spokesperson, is responding to the Russian attack at a Ukraine train station that killed at least 50, saying, "We can no longer be surprised by the Kremlin's repugnant disregard for human life."

Five children were among those killed when Russian rockets struck the station in Kramatorsk in Donetsk Oblast on Friday morning, according to Ukraine's state-owned railway company. At least 100 people were injured, according to Donetsk Oblast Gov. Pavlo Kyrylenko.

Russia has denied involvement in the attack, which occurred as "thousands" of civilians fleeing the Russian invasion were at the train station waiting to be taken to "safer regions of Ukraine," according to Kyrylenko.

"Civilians are killed when they stay in their homes, and they're killed when they try to leave," Porter said. "Actions like these demonstrate why Russia did not belong on the U.N. Human Rights Council, and they also reinforce the U.S. assessment that members of Russian forces are committing war crimes in Ukraine."

Porter declined to say if the department considers the train station attack a war crime, saying, "Assessing individual criminal liability in specific cases is the responsibility of courts, as well as other investigatory bodies. But as the secretary, Secretary [of State Antony] Blinken, has said, 'Those responsible for war crimes and other atrocities committed in Ukraine will be held to account.'"

-ABC News' Conor Finnegan