While Poland has been welcoming refugees fleeing the destruction in Ukraine, the country will eventually meet its limit on how many people it can take in, Konrad Fijolek, president of Rzeszow, Poland, a city about 60 miles from the Ukrainian border, told ABC News.

Like many cities that border Ukraine, Rzeszow, a town of about 180,000 people, has become a pathway to safety and a lifeline for millions of refugees flooding across the border from Ukraine.

Poland will be able to receive about 1.5 million people, but any more will put the country under strain, Fijolek said.

"If a million or more come, we won't be able to cope," he said.

Some estimates suggest as many as 4 million people could leave Ukraine due to the conflict, but most of the major cities in the country are already full — and officials are attempting to move refugees into smaller cities, a feat that is "not easy," Fijolek said.

So far, all the shelters set up in Poland are temporary, he added.

"We would like to avoid the view of refugee camps here," he said. "We would like people who are escaping from the war to think that what awaits here is proper camp not camps."

In addition, the mental state among the people in Poland is continuing to deteriorate, Fijolek said.

"We as local leaders would like to send the message that if there's any possible action to stop the war [find it] and then try to negotiate, because every day at the border we can see the human tragedy," he said.

-ABC News' Chris Donato and Marcus Moore

The city of Mariupol in southeastern Ukraine is without power or water after more than a week of heavy shelling and aerial attacks from Russian forces, Serhiy Orlov, deputy mayor of Mariupol, said in a press briefing Wednesday.

More than 1,200 Mariupol residents have been killed in the bombardments, Orlov said, adding that half of those killed are ethnic Russians whom Russia claims it is saving.

A huge steel mill that employs 30,000 people and a maternity hospital with 600 beds are among the obliterated structures in the strategic port city, Orlov said.

Orlov accused Russia of indiscriminately bombarding the city because its forces were unable to break through its defenses, saying that Mariupol would not surrender and calling on the outside world to help save it by imposing a "no-fly" zone.

"We understand that Mariupol was a showroom of free Ukraine -- a dynamic bustling city compared to ghost towns of the so-called DNR," Orlov said. "We must not fall. We must win and then rebuild. We can only live and develop in a free and independent Ukraine."

-ABC News' Patrick Reevell

Roughly 180,000 people have been evacuated to Russia from Ukraine, including the Russian-controlled areas of Luhansk and Donetsk in the Donbas region, according to the Russian Defense Ministry.

"As many as 5,460 people, including 1,125 children, have been evacuated from dangerous zones in various regions of Ukraine, as well as the Luhansk and Donetsk people's republics, without participation of the Ukrainian side over the past 24 hours, Mikhail Mizintsev, head of the Russian National Defense Control Center, said Wednesday. "Over 179,000 people, including 45,436 children, in total have already been [evacuated] since the beginning of the special military operation."

Mizintsev said a total of 20,961 vehicles crossed the state border of the Russian Federation, including 867 over the past day.

Mizintsev said of the citizens who evacuated to Russia, 166 were from Turkey, 41 Ukraine, 11 Egypt, eight Italy, seven Azerbaijan, six Pakistan, five India, as well as Swedish, Moroccan, and Brazilian citizens.

The U.N. High Commissioner for Refugees (UNHCR) said earlier Wednesday it has tallied 2.15 million people that have been evacuated from Ukraine since the Russian invasion began on Feb. 24, with more than half going to Poland.

Russian forces have closed in further on Kharkiv, gaining about 20 kilometers, about 12 miles, since Tuesday, a senior U.S. defense official told reporters at a press briefing Wednesday.

"It's still heavy, heavy fighting there," the official said on Day 14 of the Russian invasion. However, the U.S. does not believe Russia has "taken the city by any means," the official added.

The U.S. has not seen any significant movement toward Kyiv or Chernihiv since Tuesday, and there is still no sign of an any immanent amphibious assault on Odessa, the official said.

In southeast Ukraine, Mariupol remains isolated. Ukrainians are putting up stiff resistance, while Russians continue to bombard the city, the official said.

Russia has about 90% of its available combat power still intact, the official said. It has now launched more than 710 missiles against Ukraine -- about half being launched from within Ukraine and half being launched from within Russia, the official said.

-ABC News' Matt Seyler