Ukraine elected a new government on Sunday in the face of pro-Russian militia attacks in its east, making billionaire Petro Poroshenko their new head of state. Poroshenko immediately offered an olive branch to the restive Donetsk and Luhansk regions, promising to open talks with Moscow as well. But the last two days showed that the path to reconciliation, both internal and external, will hardly be that simple:

The president-elect of Ukraine, Petro O. Poroshenko, vowed on Monday to restore order in the country’s east, which is besieged by pro-Russian separatist violence, but said he would not negotiate with armed rebels and instead would demand swifter results from a military campaign that has achieved only limited success.

While Mr. Poroshenko has said that he would push for parliamentary elections before the end of the year, on Monday he said he saw no reason for the removal of Prime Minister Arseniy P. Yatsenyuk and other leaders of the interim government, which has been running Ukraine since the toppling of President Viktor F. Yanukovych in February.

Mr. Poroshenko also promised to mend ties with the Kremlin, citing his business connections to Russia as well as his personal relationship with President Vladimir V. Putin, who has promised to respect the Ukrainian election results. …

Mr. Poroshenko’s remarks came as rebels seized the airport in Donetsk. While Ukrainian forces appeared to have forcibly evicted the rebels from the airport later in the day, the fight illustrated the formidable obstacles Mr. Poroshenko faces in trying to stop the country from sliding further into civil war.

The serious nature of the problem with militias in eastern Ukraine became apparent during and after the vote. Armed men attempted to seize control of an international airport in Donetsk, a direct threat not just to Kyiv but also to the region. It took two days for the Ukraine military to push them back:

Pro-Russian rebels who had taken over an international airport in Donetsk have been pushed back, Ukraine’s government says. Violent clashes erupted Monday and Tuesday; at least 35 people have died. …

The violence seems to have centered on the airport but also included several other parts of Donetsk. The city’s hockey arena was set on fire, and fighting also focused on a railway station. There are conflicting accounts of the number of people killed or wounded.

Donetsk mayor Oleksandr Lukyanchenko is being quoted by several media outlets saying that 38 fighters and two civilians have died in the violence at the airport. But the Kyiv Post says 33 were killed, citing an investigator at a morgue. Reuters reports that a rebel leader told the agency, “From our side, there are more than 50 (dead).”

The leader of the Donetsk militia claims he’s still at the airport, however:

Police said Tuesday morning that all roads to Donetsk’s Sergei Prokofiev International Airport were blocked because of sporadic gunfire. A large overturned military vehicle with its front wheel blown off was lying on a residential road a few miles from the airport.

Denis Pushilin, separatist leader of the self-declared Donetsk People’s Republic, said Tuesday morning that the airport was still under rebel control, the Russian news agency Interfax reported. Pushilin also posted a YouTube video of a news conference at the occupied regional government building late Monday to counter media reports that he had fled.

In Kiev, a military spokesman told reporters that Ukrainian security forces had given another ultimatum to separatists at the Donetsk airport.

“We have posed another ultimatum to them, and if they do not surrender, we will strike them with special weapons. This is one of the proofs we are going to continue the anti-terrorist operation and bring it to its logical end,” a spokesman for the Ukrainian military’s operations in the east, Vladislav Seleznev, told reporters Tuesday. Seleznev said that around 200 pro-Russian militants attacked the airport early Monday.

CNN’ Nick Paton-Walsh calls the seizure of the airport “a bright red line.” That line was actually crossed weeks ago, but this does make it clear that neither side intends on retreating from it in the near future, despite the successful election in Ukraine. The remaining question is whether Russia will intervene against the Ukrainian military now that the election has been held and Poroshenko has embraced diplomacy with Moscow as at least a parallel track. Those pro-Russian separatist militias may end up being even more isolated than they realize.