Ukraine's Ministry of Foreign Affairs said Thursday it has appealed to the U.N. to facilitate the return of Ukrainian children who have been "illegally deported from Ukraine."

"The threat of illegal adoption of Ukrainian children by Russian citizens without following all the necessary procedures set out in Ukrainian law is glaring," the statement said. NBC News was unable to verify these claims.

“In violation of international humanitarian law and basic standards of humanity, Russia is engaged in state-organized kidnapping of children and the destruction of future of the Ukrainian nation,” it said.

Ukrainian officials have repeatedly accused Moscow of forcefully moving thousands of civilians from the besieged eastern city of Mariupol to Russia. Kremlin has denounced the accusation, alleging Kyiv has hindered evacuation efforts.

Russian forces continued shelling residential areas in Kharkiv, according to its governor, killing four people and injuring 10 others on Thursday.

“Today during the day the occupiers continued to fire on residential areas of Kharkiv, where there is no military infrastructure. These are brutal deliberate attacks on civilians,” Kharkiv Gov. Oleh Syniehubov wrote on his Telegram channel.

Syniehubov described "intense artillery strikes" on four separate residential districts. Humanitarian aid to the city of Zolochiv have also been suspended due to the shelling, the governor said.

He urged civilians to heed air raid signals, warning Russian forces were "constantly and chaotically striking at residential areas."

Russian forces are attacking Ukrainian troops in a region in the eastern part of the country on the border with Russia in preparation for a "renewed offensive," Britain's Ministry of Defence said on Thursday.

The towns of Kramatorsk and Kostiantynivka in the Donbas region are likely to be targeted with indiscriminate attacks and similar violence seen in other urban centers throughout the conflict, the ministry in its latest intelligence report.

"The combination of widespread missile and artillery strikes and efforts to concentrate forces for an offensive represents a reversion to traditional Russian military doctrine," the ministry said.

It added such an offensive would require a large number of troops, and a significant number Russian troops and equipment are tied up in and around the besieged city of Mariupol.

More than 31,000 people crossed the border into Ukraine on Wednesday, including 27,000 Ukrainians, the State Border Guard Service said Thursday.

In a Telegram post, it said that over 71,000 people and more than 16,000 vehicles left Ukraine, crossing the western borders into the European Union and Moldova.

There has been an influx of returning Ukrainians as Russian forces regroup and focus on eastern and southern parts of the country.

Border guards did not say where the non-Ukrainians coming into the country were from or what they were likely to be doing, but in the past officials have reported an influx of humanitarian workers and military volunteers.

Russia has warned it could rule out keeping the Baltics nuclear free if Finland and Sweden joined NATO, saying such a move would force it to boost its defenses in the region.

“There can be no more talk of any nuclear-free status for the Baltic — the balance must be restored,” Dmitry Medvedev, deputy chairman of Russia’s Security Council and the country's former president, said in a statement on his official Telegram channel Thursday.

In the same statement, Medvedev said the addition of Finland and Sweden to the military alliance was merely a few more opponents for Russia. "Two less, two more — with their importance and population, there is no big difference."

Finland and Sweden on Wednesday reached important stages on their way to NATO membership with the Finnish government issuing a security report to lawmakers and Sweden’s ruling party initiated a review of security policy options.

As Russia prepares for a renewed offensive in eastern Ukraine, Ukrainian resistance is "tying down" the invading troops in Mariupol, according to the British defense ministry.

In an intelligence update published Thursday, it said "the combination of widespread missile and artillery strikes and efforts to concentrate forces for an offensive represents a reversion to traditional Russian military doctrine."

Urban centers have faced indiscriminate attacks from Russia, it said, adding that the eastern towns of Kramatorsk and Kostiantynivka are likely to be targets of "similar levels of violence."

Nine humanitarian corridors will open in Ukraine on Thursday after a day of closure, Deputy Prime Minister Iryna Vereshchuk has announced.

In a Telegram post, she said that residents of the encircled city of Mariupol and Berdyansk will be able to evacuate to Zaphorizhzhia via their own transport. Five more routes to the eastern city of Bakhmut in Donetsk will be available.

“Humanitarian corridors in Luhansk region will operate provided that the shelling by the occupying forces ceases,” she said. 

No corridors were opened Wednesday as Vereshchuk said the Russian military had blocked evacuation buses in Zaphorizhzhia and violated a cease-fire in the eastern region of Luhansk.

Ukrainian officials have repeatedly accused Russia of hindering humanitarian efforts, especially out of Mariupol, where Russian forces have circled thousands of residents who remain without access to food, water, electricity and other essentials.

Ukrainian officials said their forces have damaged a Russian warship in the Black Sea with cruise missiles.

Ukrainian presidential adviser Oleksiy Arestovych said the ship, Moskva, was the same one that demanded the surrender of Ukrainian forces on Snake Island early on in the February invasion.

Russia’s defense ministry said the warship had been “seriously damaged,” but blamed the incident on a fire, according to the Russian state news agency Tass. NBC News has been unable to verify what happened on the ship.

Russia has been cracking down on the media, limiting what can be said under the threat of imprisonment.

The governor of the Odesa region in Ukraine, Maksym Marchenko, said on Telegram that Neptune missiles, which are a type of cruise missile, caused serious damage to the warship.