Russian President Vladimir Putin's order for troops to block a steel plant in besieged Mariupol remains in force, Kremlin spokesman Dmitry Peskov said Thursday.

"The Ukrainian side, especially those hiding on the premises of this plant, are well known for producing loads of lies and fakes on a permanent basis," Peskov told reporters during a daily briefing call from Moscow. "Therefore, information coming from them should be filtered very carefully."

Peskov was asked about reports from the Ukrainian side that Russian forces were storming the Azovstal Iron and Steel Works plant and heavy fighting was ongoing. Hundreds of Ukrainian fighters and civilians are said to be trapped inside the sprawling industrial site, the last pocket of resistance in Mariupol as Russian forces claim to have taken full control of the strategic Ukrainian port city.

"You bore witness to the order publicly given by the president, the supreme commander-in-chief not to begin the storm," Peskov said. "The supreme commander-in-chief did not give any other orders."

While the blockade of the Azovstal plant in Mariupol continues, Peskov also claimed that humanitarian corridors "are working there today" to allow civilians to evacuate.

Ukrainian forces have mounted successful counteroffensive pushing Russians farther away from Kharkiv.

Ukrainian presidential adviser Oleksiy Arestovych claimed Thursday that Russian artillery is now fully out of range of Kharkiv.

Shells have continued to fall on outer neighborhoods but the city center itself is now rarely hit.

Even Semyon Pegov, a prominent Russian pro-Kremlin propaganda blogger, has admitted that Ukraine is having some success around Kharkiv and that the Russian forces’ position is "getting complicated." Pegov, who has close ties to Russia’s Defense Ministry, in a post acknowledged Ukraine had retaken Stary Saltykov, a settlement near Kharkiv, and that Ukrainian artillery is now hitting Kazachya Lopan, a village on the Russian border.

Following Russia's failure in Kyiv, as Russian forces put focus on the Donbas region in the east, it also pulled back from Kharkiv, giving up efforts to seize the city and instead using a smaller artillery force to try to keep Ukrainian troops pinned down in the city.

-ABC News' Patrick Reevell

Ukrainian forces continued to shell villages in neighboring Russia's Belgorod Oblast, the regional governor claimed Thursday.

In a statement via Telegram, Belgorod Oblast Gov. Vyacheslav Gladkov alleged that Ukrainian shelling had damaged at least five homes and a power line in the villages of Zhuravlevka and Nekhoteevka, which share a border with eastern Ukraine. There were no casualties reported among civilians in the area, according to Gladkov.

"We will start working within an hour to resume power supply," Gladkov said, noting that the shelling had stopped for now. "We will also carry out the necessary measurements to restore every damaged house. No one will be left without help."

The deputy mayor of embattled Mariupol claimed Thursday that some of the city's residents are being "forcibly detained in appalling conditions" in Russian "filtration camps" in a nearby village.

"Filtration camps in the village of Bezymyanne have been turned into a real ghetto for Mariupol residents," Mariupol Deputy Mayor Petro Andryushchenko said in a statement via Telegram. "This is the most horrible story that needs to be told to the whole world. Without exaggeration, this is a new page in Russia's war crime that is happening right now."

Andryushchenko alleged that, about a month ago, Russian forces took thousands of men from several Mariupol neighborhoods, confiscated their passports and placed them in filtration camps in Bezymianny, about 20 miles from Mariupol. As for the women who were left behind, they don't leave their homes because they fear being raped by Russian troops who have settled in the area, according to the deputy mayor.

"All this once again shows the realities of the occupation," he said.

Andryushchenko posted videos on Telegram alongside his statement, purportedly showing a school in Bezymianny that he alleged Russian force are using as a filtration camp. He claimed that the detainees are forced to sleep on the floor, don't have access to medical care and can only wash themselves in a single sink with cold water. He alleged that all detainees, including the sick and those with disabilities, are forced to do landscaping work in the village. He also claimed that at least one man has died because he was refused medical assistance and another has been diagnosed with tuberculosis.

The deputy mayor alleged that the Russian military is planning to dress the detainees in the uniform of the Ukrainian military and parade them as "prisoners" during a celebration in Mariupol on Monday to coincide with Moscow's Victory Day Parade, which celebrates Russia's victory over Nazi Germany in World War II.

The Russian military claimed Wednesday to have taken complete control of Mariupol, a strategic port city in eastern Ukraine's war-torn Donetsk Oblast that has been under heavy Russian bombardment since the start of the invasion on Feb. 24. Ukrainian fighters and civilians who remain in Mariupol are holed up inside the sprawling Azovstal Iron and Steel Works plant, which has a network of underground tunnels and bunkers.

ABC News recently spoke to Denys Prokopenko, a commander of the Azov Regiment, a far-right group now part of the Ukrainian military that was among the units defending Mariupol. Prokopenko is now trapped inside the Azovstal plant with others said the fighters there have tried to initiate a cease-fire with Russian force to create conditions that would allow people to flee. But he said there are grave concerns about where those who choose to leave will end up because Russian authorities have said that all civilians will be allowed to choose to go to either Ukrainian- or Russian-controlled territory, but only after processing through Russian filtration camps.

"If our people are captured against their will and forcefully, forcibly relocated to the Russians, it's unacceptable," Prokopenko told ABC News.

-ABC News' Clark Bentson, Dragana Jovanovic, Ian Pannell and Max Uzol

At least one person -- a journalist -- was killed in a rocket attack on a residential building in Kyiv on Thursday evening, ABC News has learned.

Kyiv Mayor Vitali Kilitschko said Friday that rescuers had found the body of a victim amid the rubble.

Radio Liberty, a service of the U.S.-funded Radio Free Europe/Radio Liberty, reported that one of its employees, Vira Gyrych, was killed when a Russian missile hit her apartment in the Ukrainian capital on Thursday. Her body was found beneath the wreckage Friday morning, according to the report.

Gyrych had worked as a journalist and producer for Radio Liberty's Kyiv bureau since 2018. Prior to that, she worked for leading Ukrainian television channels, according to Radio Liberty.

"The editorial staff of Radio Liberty expresses its condolences to the family of Vira Gyrych and will remember her as a bright and kind person, a true professional," Radio Liberty said in its report.

Israeli Ambassador to Ukraine Michael Brodsky also confirmed Gyrych's death in a Twitter post, saying she was a former employee of the Israeli embassy in Kyiv.

Thursday's rocket attack came as United Nations Secretary-General Antonio Guterres visited Kyiv. Five Russian missiles flew into the city, according to Ukrainian President Volodymyr Zelenskyy. At least 10 people were injured, including four who were hospitalized, according to the Kyiv City Council.