United Nations Secretary-General António Guterres wrote separate letters to Russian President Vladimir Putin and Ukrainian President Volodymyr Zelenskyy on Tuesday asking to meet "to discuss urgent steps to bring about peace in Ukraine," a UN spokesperson said on Wednesday.

Mykhailo Podoliak, adviser to the head of the president's office, tweeted that Ukraine is ready to hold a special round of negotiations in Mariupol.

Four more Russian battalions, each made up of roughly 800 to 1,000 troops, have crossed into Ukraine over the last 24 hours, a senior U.S. defense official said Wednesday. Three of those battalions -- or up to 3,000 troops -- moved to the disputed Donbas region in eastern Ukraine, the official said.

Four flights carrying military aid, including artillery, from the Biden administration's most recent $800 million package arrived in Ukraine over the last 24 hours, the official said. More supplies are set to arrive over the next day, the official said.

When ABC News asked why the U.S. decided to send artillery, the official responded: "We're mindful of the importance of artillery in the fight that they're in right now and in the fighting in the days to come because of the terrain, and because of what we think they're going to be up against with Russian forces."

Another reason was "the fact that it wouldn't require an onerous amount of training for the Ukrainians to know how to use them" and the ability to ship them quickly, according to the official.

-ABC News' Matt Seyler

Ukraine's Deputy Prime Minister Iryna Vereshchuk said Wednesday's humanitarian corridor from Mariupol didn't work as planned but evacuation efforts will continue Thursday morning.

"Due to the lack of control over their own military on the ground, the occupiers were unable to ensure a proper ceasefire," Vereshchuk said in a statement.

There also wasn't "timely transportation of people to the point where dozens of our buses and ambulances were waiting," Vereshchuk said.

-ABC News' Alex Faul

Secretary of State Antony Blinken warned Wednesday that he thinks the atrocities in the port city of Mariupol will show to be "far worse" than in Bucha, where, after Russian troops retreated, there were found to be scores of civilians killed, and in some cases, tortured.

"We can only anticipate that when this tide also at some point recedes from Mariupol, we're going to see far worse -- if that's possible to imagine," Blinken said during a press conference in Panama.

Blinken expressed some doubts about Russia's offer of humanitarian corridors for Ukrainian civilians and service members to leave Mariupol.

"Of course, we want to see people who are in harm's way, if they're able to, leave it safely and securely," he said. "The judgment on whether the humanitarian corridor established to do that from Mariupol is safe and secure is one ultimately that the Ukrainian government is going to make … and ultimately, the decision to leave is going to be a burden on the people themselves to make that very difficult decision."

He said the U.S. is "certainly assisting" by giving its evaluations and assessments of the situation to the Ukrainian government.

But Blinken warned: "What gives pause is the fact that there have been agreements on humanitarian corridors established before that have fallen apart very, very quickly - if not immediately - principally because the security has been violated by Russian forces."

-ABC News' Conor Finnegan

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.