Ukraine's presidential elections have not restored peace in eastern Ukraine, where pro-Russian separatists continue to fight for independence and possible annexation by Russia. Moscow has denied supplying any military support to the insurrection, but reports from the region say there is growing evidence that many rebel fighters are Russian nationals, including some from Chechnya.

The ballots from Sunday's presidential election were still being counted when insurgents in the Donbas region seized the area's main airport and fought one of the fiercest battles to keep control over the city of Donetsk.

Moscow has officially endorsed the Ukrainian election. But Ukrainian officials say Russia is sending forces across the border to fight alongside the separatists, and this needs to be addressed.

"Ukraine needs to organize its defense - but not just the protection of the Ukrainian-Russian border. We need to use all government resources, especially in the Donetsk and Luhansk regions," said Nikolai Litvin, from the Ukrainian Border Patrol.

Local officials say some of the wounded fighters, hospitalized after this week's fighting in Donetsk, are Chechen nationals.

Chechnya's pro-Russian leader Ramzan Kadyrov is denying claims he sent the fighters on Moscow's orders.

But Washington-based political analyst Peter Eltsov is skeptical of this denial.

"If there are Chechens right now fighting together with the Russian separatists in Donetsk, that means just one thing: that they were sent by Kadyrov directly and they are some kind of Kadyrov's militia - Kadyrov's people," said Eltsov.

Eltsov says Russian President Vladimir Putin most likely asked his ally Kadyrov to dispatch Chechen fighters to eastern Ukraine.

"It's an incredible hypocrisy. On the one hand, Russia supports separatism within Ukraine, and at the same time fights separatism within Russia, in the case of Chechnya. So, he [President Putin] would, of course, want to show [that] we have no Chechen separatism any more and Chechens want a great Russia, and would fight even on the side of the Russian separatists in Ukraine," he said.

Eltsov says there are other signs that Chechen fighters were sent by Russia.

"They are well trained because we can see from the news that these are not just random people, these are well-trained people who have arms. Where are they getting them? They are clearly getting them from the Russian Federation," said Eltsov.

An uneasy calm has returned to the streets of Donetsk where residents spent several nights seeking shelter from the shooting.

"It is time to end this and start talks and agree on something peaceful and stop shooting from both sides," said Donetsk resident, Vasily.

But observers say the insurgents are only regrouping for their next move.