DONETSK, Ukraine - The question of fighters from Russia loomed over the insurgency in eastern Ukraine on Wednesday, as separatists acknowledged the support they are getting from foreign militiamen, and government officials in Kiev worried that the border with Russia is becoming a primary source of danger.
Casually brushing away allegations he had dispatched his paramilitaries to Ukraine, Chechnya's Moscow-backed strongman leader insisted on his Instagram account Wednesday that he was powerless to stop fellow Chechens from joining the fight.
While there is no immediate indication that the Kremlin is enabling or supporting combatants coming from Russia into Ukraine, Moscow may have to quash rumors it is waging a proxy war if it is to avoid more sanctions.
President Barack Obama was categorical about how he views the situation.
"In Ukraine, Russia's recent actions recall the days when Soviet tanks rolled into Eastern Europe," he said.
Almost daily, reports circulate in Ukraine of truckloads of gunmen crossing from Russia. Authorities believe they are a vital reinforcement to the armed rebel force that has repeatedly thwarted government operations to clear them out of seized buildings and territory in eastern Ukraine.
"Our border, especially in the Donetsk and Luhansk regions, has become a frontline that various terrorists are trying to break through," said Ukrainian border service chief Mykola Lytvyn.
The government condemns the roiling insurgency as the work of "terrorists" bent on destroying the country, while rebels insist they are only protecting the interests of eastern Ukraine's Russian-speaking population.
Russia denies mass border crossings are taking place, although separatist Donetsk People's Republic leaders now freely admit that their ragtag army includes many foreigners, including ones from the Russian province of Chechnya.
"Yes, they're not Russians, but they share much of the same ideology," said the self-proclaimed separatist "prime minister" of Donetsk, Alexander Boroday. "And you know, sometimes, representatives of the North Caucasus turn out to be even more Russian than Russians themselves."
The eastern city of Donetsk was calm but tense Wednesday, as Ukrainian fighter jets flew overhead around midday and unconfirmed reports abounded about gunfights in the center. The airport, located six miles from the heart of the city, was the scene of heavy fighting Monday, as rebels sustained heavy casualties after being pushed out of the terminal.
The Ukrainian military operation -- using jet fighter air strikes, helicopter gunships, heavy artillery and a ground assault by Ukrainian paratroopers -- was unprecedented, reports CBS News correspondent Charlie D'Agata.
Bodies piled up at the morgue. Rebel commanders have said they lost more than 100 fighters. The Ukrainian government said its forces suffered no losses in the assault.
The battle for the airport may prove pivotal for two reasons: it was the highest-profile attack separatists have launched so far, and it triggered the highest-profile response from the Ukrainian military so far.
Pro-Russian separatists have had the run of this region for a number of weeks. Armed gunmen roam the streets freely. There has been virtually no Ukrainian troop presence in Donetsk, and while there are still Ukrainian police here, neither side pays the other much attention -- the local police represent no challenge to the heavily armed gunmen.
Barricades built by supporters of the Donetsk People's Republic have now been erected at a crossroads a short distance from the government-controlled airport. There were sporadic gunfights around the airport Wednesday and Associated Press journalists saw as one man dragged away by pro-Russia militia in a nearby residential zone.
In Slovyansk, a city 55 miles north of Donetsk which that has seen constant clashes over the past few weeks, residential areas came under mortar shelling Wednesday from the government forces. Several people were wounded and some buildings, including a school, were damaged.
Authorities accuse insurgents of placing firing positions in inhabited areas, forcing the army to risk civilian lives by returning fire. Although Ukrainian troops may outnumber the rebels and have the advantage of air support, their edge is dulled by poor coordination and nervousness about engaging in urban combat.
The Donetsk People's Republic militia is a force of uncertain strength that includes units of varied provenance and abilities.
At least one militiaman participating in a celebratory parade Sunday in central Donetsk wore a patch identifying him as belonging to a Cossack unit from the North Caucasus. Others identify themselves as members of a division calling itself the Russian Orthodox Army. Many of those questioned insist they are either locals or from Crimea, the southern Ukrainian peninsula annexed by Russia in March.
Donetsk mayor Oleksandr Lukyanchenko said some fighters treated after Monday's deadly clashes were from cities in Chechnya. And it's this Chechen contingent that has aroused most alarm.
Chechnya's pro-Moscow leader Ramzan Kadyrov was a former rebel who fought Russian forces in the first of two devastating separatist wars and switched sides during the second campaign, when his father became the region's pro-Russia leader. Following his father's death in a rebel bombing, Kadyrov stabilized the region, relying on generous Kremlin funding and his ruthless paramilitary forces, which have been blamed for extrajudicial killings, torture and other abuses.
Kadyrov's forces, known for their warrior spirit and deadly efficiency, helped Russia win a quick victory in a 2008 war with Georgia. The 37-year-old leader has vowed an unswerving fealty to Russian President Vladimir Putin and hailed his policies in Ukraine.
The Chechen leader has derided allegations that he dispatched militias to Ukraine but undermined his own assertions by peppering them with veiled threats.
"If the Ukrainian authorities want so much to see 'Chechen units' in Donetsk, why go to Donetsk, if there is a good highway to Kiev?" he said in Wednesday's statement.
If an unspecified number of armed Russian citizens are now in Ukraine, it's far from evident they have Moscow's outright blessing.
The Kremlin welcomed Ukraine's presidential election and said it was ready to work with the winner, billionaire candy magnate Petro Poroshenko. That was an apparent bid to de-escalate the worst crisis in relations with the West since the Cold War and avoid a new round of Western sanctions.
Fyodor Lukyanov, editor of Russia in Global Affairs Magazine, wrote this week that Moscow knows that support for insurgents in Ukraine could translate into punitive Western actions. He argued Moscow would instead likely seek guarantees instead that Ukraine will not join NATO.
But Gleb Pavlovsky, a political strategist who has advised the Kremlin in the past, warned that the insurgency in the east has gained enough momentum to keep going without Moscow's orders.
"It shouldn't be seen as being controlled by one button. You can push this button once, but you can't push it again to recall the command," he said on Ekho Moskvy radio.
Still, it is unclear what a realistic goal might be for the insurgency, since even Russia has proven reluctant to publicly grant its patronage. Denis Pushilin of the Donetsk People's Republic was compelled again Wednesday to issue a plea for Russian support after a previous call went unheeded.
"We are waiting for help from a brother nation, a brother state. We are Russians, and that is exactly why we are being killed. We want to become part of Russia," Pushilin said.
Russia has supported a peace plan by the Organization for Security and Cooperation in Europe that calls for ending hostilities and launching a political dialogue. It accuses Ukraine of failing to observe the plan, despite the fact that Ukraine has held round-table talks on the country's future in several cities in the last two weeks.