(NewsNation) — Russian armed forces continued Tuesday to hammer away at cities throughout Ukraine — but were still unable to overrun most of them — as the conflict approached its third week.

In the beseiged Ukrainian port city of Mariupol, Russian troops seized a hospital late Tuesday and took about 500 people hostage, regional leader Pavlo Kyrylenko said.

Russians troops drove 400 people from neighboring houses into Regional Intensive Care Hospital, Kyrylenko said on the messaging app Telegram. About 100 doctors and patients also are believed to be inside, he said.

The troops are using those inside the hospital as human shields and are not allowing anyone to leave, he said.

“It’s impossible to leave the hospital, they are shooting hard,” Kyrylenko said.

Kyrylenko said the main building of the hospital has been heavily damaged by shelling, but medical staff are continuing to treat patients in makeshift wards set up in the basement.

He called on the world to respond to these “gross violations of the norms and customs of war, these egregious crimes against humanity.”

The Ukrainian army’s General Staff says Russian troops are trying to block off the city from the western and eastern outskirts of the city. “There are significant losses,” it said in a Facebook post.

In other developing war news:

Ukraine said a fourth Russian general has been killed in the fighting.

Maj. Gen. Oleg Mityaev died Tuesday during the storming of Mariupol, said Ukrainian Interior Ministry adviser Anton Gerashchenko, who published a photo on Telegram of what he said was the dead officer.

Ukrainian President Volodymyr Zelenskyy reported the death of another Russian general in his nighttime address but didn’t name him.

Mityaev, 46, commanded the 150th motorized rifle division and had fought in Syria, Gerashchenko said.

There was no confirmation of the death from Russia.

Russian warships fired missiles and artillery at the Ukrainian sea coast near Tuzla, to the south of Odesa, Interior Ministry adviser Anton Gerashchenko said.

“They fired a huge amount of ammunition from a great distance,” he said on Facebook.

Gerashchenko said Russia wanted to test Ukraine’s coastal defense system.

He said there was no attempt to land troops. He didn’t say whether any of the shelling hit anything.

The leaders of Poland, the Czech Republic and Slovenia traveled to Ukraine’s capital Tuesday on a European Union mission to show support for the country. They took a train from Poland, meeting with the Ukrainian president Tuesday evening as a curfew began in Kyiv and explosions could be heard in the distance.

“The aim of the visit is to express the European Union’s unequivocal support for Ukraine and its freedom and independence,” Czech Prime Minister Petr Fiala said in a tweet.

A BBC report quoted a tweet from Ukraine’s Prime Minister Denys Shmyhal, saying “devastating” sanctions against Russia had been discussed, including the “recognition of Russia as a sponsor of terrorism.”

Russia has stepped up its assault on Ukrainian cities with artillery strikes on Irpin and the northwest Kyiv suburbs of Hostomel and Bucha, said the head of the capital region, Oleksiy Kuleba. The second-largest city, Kharkiv, was also hit with more than 60 strikes.

And yet, almost three weeks into the conflict, Russian troops haven’t been able to overrun the capital city of Kyiv, or even Kharkiv, the nation’s second largest city located close to the Russian border. And this is despite the fact that the Russian army is far larger and better equipped than their Ukrainian counterparts.

Retired U.S. Lt. Gen. Richard Newton, a Tuesday guest on NewsNation’s “Dan Abrams Live,” said of the Russian military: “In terms of a March Madness basketball vernacular … a lot of us thought they were 6’5″ but really they’re only 5’5.”

Maria Shuvalova, a university professor in Kyiv, said on Tuesday’s “NewsNation Prime” that the tenacity of Ukranian fighters should come as no surprise.

“It’s our history. My grandparents survived artificial famines made from Russians. At every lesson of history, Ukrainian literature, you’re facing Russia excoriating Ukrainian culture. Ukrainian history is a history of massive resistance, so we have experience of staying strong for as long as we can.

Zelenskyy is seeking to extend martial law until April 24 and to require men ages 18 to 60 to stay in the country to fight. Zelenskyy submitted the extension in a bill to Parliament, which is expected to vote on it this week.

The latest negotiations between Russian and Ukrainian diplomats, held via video conference, were the fourth round involving higher-level officials from the two countries and the first in a week.

The two sides had expressed some optimism in the past few days. Mykhailo Podolyak, the aide to Zelenskyy, tweeted that the negotiators would discuss “peace, cease-fire, immediate withdrawal of troops & security guarantees.”

NATO adviser Dmitri Alperovitch, a Tuesday guest on “NewsNation Prime,” noted that Zelenskyy’s comments regarding the negotiations with Russia are taking on an increasingly optimistic tone.

Zelenskyy is “now saying he doesn’t think Ukraine will ever join NATO, and NATO doesn’t want Ukraine. That of course was one of the big sticking points Vladimir Putin demanded — this neutrality for Ukraine. If Zelenskyy’s willing to concede on that he might have a path for a cease-fire.”

In Washington, White House press secretary Jen Psaki said that while President Joe Biden’s administration supports Ukraine’s participation in the talks, Russian President Vladimir Putin would have to show signs of de-escalating in order to demonstrate good faith.

Russia also sanctioned President Joe Biden and several members of his administration, including press secretary Jen Psaki. She shrugged off the move at a Tuesday media briefing.

“It won’t surprise any of you that none of us are planning tourist trips in Russia. None of us have bank accounts that we won’t be able to access,” she said. “So we will forge ahead,”

Hillary Clinton was also sanctioned, and she tweeted, “I want to thank the Russian Academy for this Lifetime Achievement Award.”

The situation in Ukraine is still developing and dangerous. In an area outside Kyiv, Fox News reporter Benjamin Hall was injured while reporting and was hospitalized. On Tuesday, the network said Pierre Zakrzewski, a cameraman, was killed this week while covering the invasion.

Zakrzewski and Hall’s vehicle was struck outside Kyiv by incoming fire, Fox News Media CEO Suzanne Scott said in a memo to employees.

In Washington, D.C., legislators prepared for a livestreamed address Wednesday by Zelenskyy. The speech may be among the most important in a unique and very public strategy in which he has invoked Winston Churchill, Hamlet and the power of world opinion in his fight to stop Russia.

Though the US has ruled out sending American troops to directly participate in combat, Zelenskyy is sure to find a receptive audience in Washington. In a rare display of bipartisan unity, the U.S. Senate has voted unanimously to condemn Putin as a war criminal. The rare cross-party vote called on the International Criminal Court at The Hague to probe Putin’s decision to invade Ukraine.

The Associated Press and Reuters contributed to this report.