Russia to redeploy Kyiv forces, not withdraw, US official says: LIVE UPDATES

President of Ukraine Volodymyr Zelenskyy expresses caution during nightly address.

"The signals we hear from the negotiating platform can be called positive. But these signals do not drown out the ruptures of Russian shells," he said after 34 days of warring with Russia.

A funeral service was held on Tuesday for veteran Fox News cameraman Pierre Zakrzewski, who was killed while reporting on the ground in war-torn Ukraine. 

FOX News Media CEO Suzanne Scott told staff that a small group from the company would be attending the service held at the Church of Our Lady of Perpetual Succour in Dublin suburb of Foxrock.

Over 100 of Pierre's colleagues and loved ones from around the world wrote messages in an online condolence book. 

Read more: Funeral held for Fox News cameraman Pierre Zakrzewski in Ireland

Russian media acknowledged Tuesday that two border villages had to be evacuated because of shelling from Ukraine, one of the first signs that Ukraine has begun to take the fight across the border and into Russia.

Interfax, a Russian government controlled publication, reported that a possible shell from Ukraine exploded in the village of Zhuravlyovka, resulting in some injuries and a home being destroyed.

The shelling forced evacuations of Zhuravlyovka and nearby Niekhoteyevka to the Russian town of Belgorod, displacing about 180 people.

The report indicated that the explosion was not an accident, though it did not confirm that the explosion was due to hostile fire from Ukraine.

RIA Novsti, another Russian publication friendly to the Kremlin, also reported on an explosion near the two towns that injured four, people saying the attack originated from Ukraine.

Fox News cannot independently verify the reported attacks within Russia, though the reports are originating from Russian media outlets.

Russian forces have kicked up radioactive dust and disturbed a highly toxic zone around the area of the Chernobyl nuclear disaster site known as the "Red Forest" since capturing the defunct power plant early on in its invasion of Ukraine, workers at the site said. 

Reuters spoke with workers who said Russian soldiers in a convoy did not use anti-radiation gear and inhaled toxic dust that will most likely cause internal radiation in their bodies. In the weeks after Russia took the site on Feb. 24, soldiers were still not wearing any protective gear, they said. 

Two workers were on duty when Russian forces took control of the Chernobyl power plant, the site of the 1986 nuclear disaster that's considered the worst in history and became an international embarrassment for the Soviet Union. The Red Forest, a small area surrounding the power plant, is still highly contaminated.

Read more: Russian soldiers disturbed radioactive dust at Chernobyl; didn’t wear protective gear, workers say: report

Ukrainian forces shelled a Russian military camp inside Russia, according to reporting from the New York Post. Such a strike would be the first time Ukraine struck Russia on the other side of the border.

The strike hit the military camp near the Russian city of Belgorod, which sits about 50 miles from the Ukrainian city of Kharkiv near the Russian border.

Video posted online of the reported attack appeared to show ammunition blowing up, though the source of the explosion has yet to be confirmed.

Four people were reportedly injured in the explosion.

Pentagon Press Secretary John Kirby said Tuesday that the U.S. has seen "increased activity" and "offensive activity" by Russian forces in the Donbas region of Ukraine.

The Donbas region, which has a large population of Russian-speaking citizens, has been at the center of tension in Ukraine for much of the conflict. Before launching its full-scale invasion of Ukraine, Russia moved to acknowledge claims of independence by separatists groups in the region.

Ukraine is seeking concrete security guarantees during peace talks in Turkey, saying they want countries to promise to intervene during conflicts in Ukraine.

"The Treaty on Security Guarantees essentially assumes, not in theory, but in practice, to obtain an effective instrument for protecting our territory and sovereignty," Mihailo Podolyuak, top adviser to Ukrainian President Volodymyr Zelenskyy, said of the talks. "The guarantor countries become, so to speak, the leading armies of the world, including those with a nuclear component, which take on specific legal obligations - to intervene in any conflict on the territory of Ukraine, to immediately supply weapons."

Ukraine and Russia said they have made progress in the talks, according to reporting from the Wall Street Journal, with Ukraine willing to take on a "neutral status" militarily while looking for admission into the European Union's free-trade zone.

Pentagon Press Secretary John Kirby said that the Russians have failed to take the Ukrainian capital of Kyiv, which he said was an objective for their forces.

Kirby said that a small number of Russian troops are now moving away from Kyiv, though he wouldn't classify it as a retreat or withdrawal of forces and Kyiv continues to be the target of air strikes.

The press secretary also noted that the Russians have failed in their objective to take most Ukrainian population centers, in large part because of fierce Ukrainian resistance.

President Biden said the United States will continue to provide the Ukrainian military with "the capacity to defend themselves" and will monitor whether Russia will "follow through" on its claims early Tuesday that they are beginning to withdraw forces from Ukraine’s Kyiv region.

The president, during a joint press conference at the White House Tuesday with Singapore Prime Minister Lee Hsien Loong, was asked about Russia’s announcement that it would "fundamentally scale back" its military operations near Ukraine’s capital city of Kyiv.

"I don't read anything into it until I see what their actions are," Biden said. "We'll see if they follow through on what they’re suggesting."

Read more: Biden: US to continue giving Ukraine 'capacity to defend' itself as Russia claims troop withdrawal from Kyiv

The young Ukrainian couple who captured hearts around the world when they married early amid Russia's invasion and immediately joined the war effort continue to be optimistic about Ukraine's future, but they are asking for help to gather supplies.

Yaryna Arieva, 21, and her 24-year-old husband, Sviatoslav Fursin, married as soon as Russia's invasion began in February, months ahead of their planned wedding date, and joined Ukraine's Territorial Defense Forces immediately after their wedding. The couple live in Kyiv, Ukraine's capital, where Russian officials say they plan to scale back military operations after more than a month of fighting.

"We will still be fighting until the last drop of blood, but if Ukraine falls, then someone will be next. Russia never stops," Arieva told Fox News Digital. "They have nothing. They have nothing to feed their people, but still, they will try to take other countries and bring their Russian world – and the Russian world looks like complete [destruction] and fear."

For more on this story: Optimism in Kyiv: Ukrainian newlyweds say they will fight until the 'last drop of blood'

President Joe Biden, during a 53-minute phone call Tuesday with the leaders of France, Germany, Italy and the United Kingdom, "affirmed their determination to continue raising costs on Russia for its brutal attacks in Ukraine, as well as to continue supplying Ukraine with security assistance to defend itself against this unjustified and unprovoked assault," the White House says.

"They reviewed their efforts to provide humanitarian assistance to the millions affected by the violence, both inside Ukraine and seeking refuge in other countries, and underscored the need for humanitarian access to civilians in Mariupol," the White House added. "They also discussed the importance of supporting stable energy markets in light of current disruptions due to sanctions."

Biden, when asked by a reporter Tuesday for his reaction to Russia's claims that it will draw down its military presence in two Ukrainian regions including Kyiv, said "We'll see if they follow through. ... Let's just see what they have to offer."

Fox News' Paul Connor contributed to this report.

A U.S. official tells Fox News' Mark Meredith Tuesday that "any movement of Russian forces from around Kyiv is a redeployment, not a withdrawal, and the world should be prepared for a major offensive against other areas of Ukraine."

“No one should be fooled by Russia’s announcements," the official said. "It also does not mean the threat to Kyiv is over. Russia has failed in its objective of capturing Kyiv, and failed in its objective of subjugating all of Ukraine, but it can still inflict massive brutality on the country, including Kyiv.”

Russia announced earlier today that it was withdrawing forces from the Kyiv and Chernihiv regions in hopes of laying the groundwork for a peace deal with Ukraine.