A member of a Ukrainian volunteer battalion looks through binoculars near the small southern Ukrainian city of Novoazovsk. (Alexander Khudoteply/Agence France-Presse via Getty Images)

The day after the leaders of Russia and Ukraine exchanged a chilly handshake at a regional summit and pledged some cooperation in their ongoing crisis, military leaders in Ukraine charged that Russia was deepening its foray into Ukrainian territory and sending new troops to the Crimean border.

In Washington, an administration official accused Russia of prevaricating over its role.

Andriy Lysenko, a spokesman for the Ukrainian military, said Ukrainian troops are battling combined Russian and separatist forces on a new, southern front around the border town of Novoazovsk, east of Crimea on the Sea of Azov. He also said Russian troops are increasing surveillance from northern Crimea, the autonomous Ukrainian peninsula annexed by Moscow in March.

As firefights and shelling continued all day, there were differing reports on whether Novoazovsk, a previously quiet border town, had fallen to Russian-backed separatists. Russian troops and their allies do control villages north of there, Lysenko said.

Referring to a “Russian-directed counteroffensive,” State Department spokeswoman Jen Psaki said Wednesday, “Clearly, that is of deep concern to us, but we’re also concerned by the Russian government’s unwillingness to tell the truth, even as its soldiers are found 30 miles inside Ukraine.”

Ukraine accused Russia of launching a new military incursion across its eastern border, as hopes quickly fade that talks between their two presidents might mark a turning point. (Reuters)

On Tuesday, Russian officials for the first time acknowledged that they had troops on the ground in Ukraine but said that 10 paratroopers captured this week had wandered across the border by mistake.

At his news briefing Wednesday, Lysenko showed a new video of the Russian paratroopers. Their deputy commander, Sgt. Vladimir Sevasteev, said he and his colleagues had “illegally come into the territory of Ukraine” while engaged in what they thought was a military exercise and wanted to be sent home to Russia.

“Please help us,” he said. “We don’t want to shoot at Ukrainian people.”

Russian President Vladimir Putin and Ukrainian President Petro Poroshenko had pledged cooperation Tuesday evening on tightening Ukraine’s eastern border and ensuring humanitarian relief for besieged residents.

And even as reports of Russians tanks and soldiers on the ground in Ukraine continued to come in Wednesday, Russian Foreign Minister Sergei Lavrov said Russia does not want Ukraine to break apart.