Ukraine said its forces had captured a group of Russian paratroopers who had crossed into Ukrainian territory on a "special mission" - but Moscow said they had ended up there by mistake.
The Ukrainian military meanwhile reported pro-Russian separatist forces were shelling the town of Novoazovsk and buildings there, including a hospital, were ablaze.
Twelve Ukrainian soldiers had been killed and 19 wounded in the past 24 hours, military spokesman Andriy Lysenko said.
Earlier, the security services released video footage purporting to show testimonies from Russian paratroopers who were detained by Ukrainian government forces while fighting alongside pro-Moscow rebels in Ukraine.
The videos, the strongest evidence yet to back up Kiev's claims of Russian involvement in the conflict, and the intensified fighting in the east overshadowed a meeting between Ukrainian President Petro Poroshenko and Russia's Vladimir Putin in the Belarussian capital Minsk.
Russia denies giving military help to the separatist rebellion in eastern Ukraine.
A Russian defence ministry source, quoted by RIA Novosti, said the servicemen had strayed into Ukrainian territory by mistake during border patrol.
Ukraine rejected this.
"It wasn't a mistake, but a special mission they were carrying out," Lysenko said in a briefing.
In footage posted on Kiev's Anti-Terrorist Operation Facebook page, one of the detained soldiers, who identified himself as Ivan Milchakov, listed his personal details, including the name of the paratroop regiment he said is based in the Russian town of Kostroma.
"I did not see where we crossed the border. They just told us we were going on a 70-kilometre march over three days," he said.
"Everything is different here, not like they show it on television. We've come as cannon fodder," he said in the video.
Another man in the footage, who gave his name as Sergeant Aleksei Generalov, said: "Stop sending in our boys. Why? This is not our war. And if we weren't here, none of this would have happened. They would have sorted things out with the government themselves."
Social networking pages appear to corroborate the men's assertions they are actively serving in the Russian military.
Photographs posted by an Ivan Melchakov of himself on Russia social media site Vkontakte are recognisable as the same person who appears in the video released by Ukraine's SBU under the name Milchakov. His page is filled with pictures of soldiers in camouflage.
Aleksei Generalov's profile photo on the site Odnoklassniki shows him smiling into the camera in military fatigues, while the Vkontakte page of another detained soldier, named as Egor Pochtoev, shows him in paratrooper uniform and a post that he is "on assignment."
The Russian soldiers were detained with their personal documents and weapons, near the small town of Amvrosiyivka in Donetsk region, the Ukrainian state security service said.
Lysenko also said Russian Mi-24 helicopters had fired on a border post on Monday, killing four border guards, while rebel attacks on Novoazovsk were happening "at this very minute."
Rebel forces, backed by an armoured column which the Ukrainian military said moved across the border from Russia, began attacking Novoazovsk on Monday aiming to open up a new front in the south.
Government forces in the five-month conflict have largely hemmed in separatist forces into the two main regional towns of Donetsk and Luhansk - a situation the separatist are trying to break out of.
Local resident Oleksiy said by phone on Sunday morning he saw a convoy of 18 armoured vehicles without insignia on Ukrainian territory 15 km from the Russian border to the south of the village of Koloski, which is not far from where the paratroopers were detained.
This corresponds with the alleged route of the paratroopers captured in Ukraine. The soldiers departed from Russia's Rostov region on Sunday at 3 a.m., the Ukrainian security service said.
"Officially they are on military exercises in various corners of Russia. In reality they are involved in military aggression against Ukraine," Defence Minister Valeriy Heletey said in a Facebook post.