Ukraine said Monday its forces had pushed back Russian troops in the Kharkiv region in a counter-offensive that allowed the Ukrainians to reach the Russian border.

The Ukrainian defense ministry posted a video showing what it said were its troops at the border, with one soldier telling Ukrainian President Volodymyr Zelenskyy, "We are here."

A senior U.S. Defense official said the Ukrainian troops were within three or four kilometers of the Russian border.

After repelling Russian advances on Kharkiv, Ukraine's second-largest city, Ukrainian forces have regained territory in the region and sought to push Russia from its staging area in Izyum as it focuses on the eastern Donbas region.

"Kremlin dreamed of capturing Kyiv, Kharkiv and Odesa, then at least the Donetsk and Luhansk regions," Zelenskyy adviser Mykhailo Podolyak tweeted Monday. "Now, Russian troops are concentrated on the Luhansk region due to lack of forces. We continue the treatment of imperial megalomania and make Moscow face reality."

Ukrainian servicemen take rest in a recently retaken village north of Kharkiv, east Ukraine, May 15, 2022

Zelenskyy said in a video address late Sunday that Ukraine was preparing for new Russian attacks in the Donbas and southern Ukraine.

"The occupiers still do not want to admit that they are in a dead-end and their so-called 'special operation' has already gone bankrupt," Zelenskyy said.

In Washington, the senior U.S. defense official reported heavy artillery fighting Monday in Donetsk, but said Russian gains were 'uneven, slow, incremental, short and small.'

'We do know that the Russians continue to take casualties," the official said. "They continue to lose equipment and systems every day.'

Western countries allied with Ukraine are continuing to send more weaponry to Kyiv's forces, with10 deliveries via airlift from seven nations in past 24 hours, the U.S. defense official told reporters during a background call Monday.

Russian President Vladimir Putin warned the West Monday that Moscow would respond if NATO bolsters its military presence in Finland and Sweden after the two Nordic countries declared Sunday they want to join the U.S.-dominated Western military alliance.

Putin told leaders of a Russian-dominated military alliance of former Soviet states that the expansion of the 30-nation NATO was being used by the United States in an 'aggressive' way to aggravate world stability.

The Russian leader said there was no direct threat from NATO by adding the two countries to its alliance but said, 'The expansion of military infrastructure into this territory would certainly provoke our response."

'What that (response) will be - we will see what threats are created for us,' Putin said at the Grand Kremlin Palace. 'Problems are being created for no reason at all. We shall react accordingly.'

Finnish President Sauli Niinisto and Prime Minister Sanna Marin announced the NATO membership bid Sunday at the presidential palace in Helsinki.

"This is a historic day," Niinisto said. "A new era begins."

Hours later, Sweden also said it would seek NATO membership, ending two centuries of military non-alignment. On Sunday, Sweden's governing party dropped its opposition to joining the military alliance.

On Monday, Swedish Prime Minister Magdalena Andersson told lawmakers in parliament that joining NATO was 'a historic change in our country's security policy.'

'We will inform NATO that we want to become a member of the alliance,' she said. 'Sweden needs formal security guarantees that come with membership in NATO.'

A building damaged by multiple shelling stands in Kharkiv, Ukraine, May 15, 2022.

The two Nordic countries' NATO applications will likely move swiftly, with the alliance's secretary-general, Jens Stoltenberg, saying in recent days that they will be welcomed.

"Finland and Sweden are already the closest partners of NATO," NATO Deputy Secretary-General Mircea Geoana said Sunday in Berlin, where members were meeting to discuss their continued support of Ukraine against Russia's invasion and the expansion of the Atlantic alliance.

Russia cut off electricity to Finland in apparent retaliation for its bid to join NATO. Finland gets 10% of its energy from Russia and the void is now being filled by Sweden.

Turkey initially expressed concerns about Finland and Sweden joining the security alliance, but Saturday said it isn't closing the door on the possibility. Any NATO enlargement requires the unanimous consent of the existing members.

"I'm not that worried," Niinisto said of Turkey's stance.

NATO and the United States said Sunday they both were confident that Turkey would not stand in the way of Finland and Sweden joining NATO. Turkish officials Sunday told foreign ministers in Berlin they want the Nordic countries to halt support for Kurdish militant groups present in their territory, and lift bans on some sales of arms to Turkey.

The top diplomats from the U.S. and Ukraine met Sunday in Berlin to talk about Russia's invasion and the impact it has had not only on Ukraine, but the rest of the world.

U.S. Secretary of State Antony Blinken assured Ukrainian Foreign Minister Dmytro Kuleba of the support that Ukraine has from its allies and discussed this week's Group of Seven industrialized nations and NATO foreign ministerial meetings.

Cindy Saine contributed to this report. Some information for this story came from The Associated Press, Agence France-Presse and Reuters.

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