Ten Russian paratroopers captured on Ukrainian territory made for an awkward summit Tuesday evening between the presidents of the two nations.

Hopes for a breakthrough at the meeting between Petro Poroshenko of Ukraine and Vladi­mir Putin of Russia already had dimmed, but when Ukraine announced early in the day that it had seized the Russian soldiers in the Donetsk region — and had video evidence — it led to what the summit host called a “difficult” discussion.

Still, the two presidents met one-on-one for two hours after a broader, six-hour session in Minsk, Belarus.

Following the meeting, Poroshenko said a “roadmap” will be prepared to end the fighting between troops and pro-Russian separatists in the east of the country, the British Broadcasting Corporation reported.

“A roadmap will be prepared in order to achieve, as soon as possible, a ceasefire regime which absolutely must be bilateral in character,” he said.

Afterward, Putin said he had told Poroshenko that Kiev must take the initiative in working out a peace agreement with pro-Russian separatists in eastern Ukraine. “We talked about the need to end bloodshed as soon as possible, about the need to shift towards political resolution of all issues,” Putin told journalists in Minsk, according to the Reuters news agency. “Russia, for its part, will do everything to support this peace process if it starts.”

But the capture of the Russian paratroopers left Moscow more exposed as a participant in the fighting in Ukraine than it has sought to portray itself. Having previously derided Kiev’s claims of Russian intervention in the separatist war in eastern Ukraine, Moscow this time simply claimed that the paratroopers had entered Ukraine by mistake. Putin noted that Ukrainian soldiers had wandered into Russia earlier this month.

But the incursion — or act of unintentional trespassing — followed Russian moves that have provoked a strong reaction among American officials.

“The new columns of Russian tanks and armor crossing into Ukraine indicates a Russian-
directed counteroffensive may be underway,” tweeted the U.S. ambassador to Ukraine, Geoffrey R. Pyatt.

“What we have seen are repeated provocations by the Russian regime to further escalate tensions in the region,” White House press secretary Josh Earnest told reporters. He called Russian intervention in Ukraine, including the sending of a humanitarian convoy without Kiev’s permission, “a pretty flagrant escalation of this situation.”

Putin and Poroshenko did reach an agreement on how to distribute aid to civilians in the separatist Luhansk region, the Interfax news agency reported. But Putin said that Russia could not discuss the terms of a cease-fire with Ukraine.

They agreed to resume talks on sending gas through Ukraine to Europe, Putin said afterward — a conversation that ran off the rails at various stages after Russia jacked up gas prices for Kiev by more than 40 percent this spring and Ukraine threatened to block all Russian gas exports through Ukrainian territory.

Russian military allegedly enters and attacks Ukrainian forces.

At the public session of the Minsk meeting, which included representatives from the Eurasian Customs Union of Russia, Belarus and Kazakhstan, as well as the European Union, Putin virtually ignored the conflict in Ukraine, except to say that he is against military escalation, and focused on economic concerns.

He warned of the potential harm to Russia and its customs union partners if Ukraine proceeds with a trade agreement with the E.U. Moscow fears that European manufacturers would ship goods through Ukraine, re-label them and avoid customs duties. Putin threatened Ukraine with unspecified consequences if it moves ahead on the trade pact. Poroshenko has said he wants the Ukrainian parliament to ratify the agreement in September.

That trade agreement has been at the center of the Ukrainian crisis. When, under Russian pressure, then-President Viktor Yanukovych backed away last fall from signing it, the protests that led to his ouster broke out. After he fled to Russia in February, Moscow’s forces seized Crimea, and the separatist movement in the east sprang into action.

Catherine Ashton, the European Union’s top security and foreign affairs official, told reporters that the participants in the first, broader meeting had not “directly discussed” the Ukrainian videos depicting the apprehended soldiers.

But the recordings were revealing.

One paratrooper named Sergei Smirnov said in an interrogation video that he was a “contractor” in the Russian army who had come to Ukraine “for training.” He added that he did not know he was in Ukraine until “we went through a village and saw a Ukrainian tank.”

Ukrainian military spokesman Andriy Lysenko told a briefing in Kiev on Tuesday that the detained Russian soldiers said they took a train to the Rostov region in Russia on Aug. 23 and joined “a march” around 3 a.m. the following day in a column of dozens of armored personnel carriers. The soldiers said that only the commanders knew they were going into Ukraine; the soldiers thought they were going for training.

Asked about the assertion by Russian officials that the troops had accidentally crossed the border, Lysenko said: “If elite troops do not know topography and do not know their locality, I can say nothing about that. . . . We believe that was not a mistake.” Rather, he said, it was “a special task executed.”

The soldiers have been “detained” but are not prisoners, Lysenko said. Ukraine has launched a criminal investigation into their activities.

Lysenko also said that for the first time since the conflict began, Ukrainian border guards were fired at on Monday in the Luhansk region by two Russian military helicopters. Four border guards died and three were injured, he said.

The incident came just days after Russia sent a convoy of humanitarian aid trucks — whose purpose, even now, is murky — into Ukrainian territory, provoking international condemnation. The Russian government said Monday that it would send a second convoy, and its path may be smoother if the agreement between Putin and Poroshenko sticks.

Gowen reported from Kiev. Alex Ryabchyn in Kiev contributed to this report.