Ukrainian forces appear to have had several successes Sunday, retaking several villages and towns in the northern and eastern parts of the country as they continue to wage fierce counterattacks against Russian troops, according to Ukrainian officials.

Ukrainian authorities claimed their troops have retaken control of some villages around Malaya Rogan near Kharkiv in the east, close to the Russian border.

Ukrainian forces also drove Russian troops from the town of Trostyanets in northern Ukraine between Kharkiv and the strategic city of Sumy, according to the mayor of Trostyanets. Video posted online appeared to show Ukrainian troops in Trostytanets.

There is also a report from Ukrainian officials that two villages were retaken near Mykolaiv in the south, where Ukrainian forces have launched a counterattack near the Russian-occupied city of Kherson.

-ABC News' Patrick Reevell

More than 3.8 million people have been forced to flee Ukraine since Russian forces invaded on Feb. 24, according to the latest figures from the United Nations refugee agency.

The tally from the U.N. High Commissioner for Refugees (UNHCR) amounts to just over 8.6% of Ukraine's population -- which the World Bank counted at 44 million at the end of 2020 -- on the move across borders in 32 days.

More than half of the refugees crossed into neighboring Poland, UNHCR figures show.

-ABC News' Christine Theodorou

Ukraine and Russia have agreed to hold a new round of in-person peace talks, in Turkey this week, in a sign of some possible progress.

A member of Ukraine's delegation said the talks would take place March 28-30, while Russia's lead negotiator said they wouldn't start until March 29.

The two sides have been talking every day by video conference, officials said.

David Arakhamia, a member of the Ukrainian parliament and part of the country's delegation negotiating with Russia, wrote on Facebook that in the last video discussions with his Russian counterparts, the parties agreed to meet in-person.

Previous in-person peace talks were held in Belarus.

Ukraine is insisting on security guarantees from western countries in any deal, with its lead negotiator telling a German newspaper over the weekend that such guarantees "don't make sense" without the involvement of the United States.

-ABC News' Patrick Reevell

Sixty tons of food and relief items have arrived in the bombed-out city of Kharkiv in northeast Ukraine, according to the International Committee of the Red Cross.

The badly needed humanitarian aid arrived on Saturday and includes food, water and essential hygiene items, ICRC officials said. The Ukrainian Red Cross will distribute the supplies to residents in the war-torn area, many taking shelter in the city's metro station.

Maxime Zabaloueff of the ICRC said the aid will go to help "the people who have suffered the terrible consequences of the shelling on this city."

The ICRC is boosting its humanitarian response in Kharkiv, Kyiv, Poltava, Dnipro, Odessa and other areas across the country to address a growing humanitarian crisis, Zabaloueff said.

The ICRC has also dispatched more than 140 additional staff to the region, including surgeons and other medical workers, psychologists, weapon contamination specialists and engineers.

All Russian troops have left the Ukrainian cities of Kyiv and Chernihiv, withdrawing north toward the borders of Belarus and Russia to consolidate before likely redeploying to the Donbas region in eastern Ukraine, a senior U.S. defense official told reporters Wednesday.

But even with the Russians gone, the territory remains treacherous.

"There are some indications that they left behind mines and things like that, so the Ukrainians are being somewhat careful in some areas north of Kyiv as they begin to clear the ground and clear the territory and re-occupy it," the official said.

While the U.S. hasn't yet seen these troops redeploy elsewhere in Ukraine, it'll likely happen soon, according to the official. Ukrainian forces are preparing for a major fight in Donbas, the official said.

The official also said the Pentagon is "monitoring" an apparent nitric acid explosion in Ukraine's Luhansk region, which Russia blamed on Ukraine.

"We've seen the Russians claim that this was a Ukrainian attack on this. We do not believe that is true," the official said. "We do believe that the Russians are responsible, but exactly what they used when they did it, why they did it, what the damage is, we just don't have that level of detail," the official said.

The official also noted that a small number of Ukrainians currently in the U.S. for "professional military education" were pulled aside for a couple days of training on Switchblade drones, which the U.S. is sending overseas as part of its military aid, according to the official.

"Although it's not a very difficult system to operate, we took advantage of having them in the country to give them some rudimentary training on that," the official said.

-ABC News' Matt Seyler