Russian President Vladimir Putin and Ukrainian President Petro Poroshenko met Tuesday in Minsk, Belarus, for a summit with hopes that the international community will help bring peace between the two countries.

At their first meeting since June, both leaders came to the table with demands that the other may find hard to meet, according to a Reuters report.

Putin advised the Ukrainian leader not to continue the advance against pro-Russian separatists in eastern Ukraine and threatened economic retribution for Ukraine signing a trade deal with the European Union.

Poroshenko countered by demanding that Russia stop sending weapons to the rebel fighters.

The two leaders shook hands to start the meeting, though tensions likely were high after Ukraine claimed on Tuesday morning that it had captured Russian soldiers that had entered Ukrainian territory, The Wall Street Journal reported.

A source in the Russian defense ministry claims that the border crossing had been an accident.

Russia continued to deny that it has been providing arms to assist the separatist movement in eastern Ukraine. The U.S. and the EU also have made these allegations and imposed sanctions that have seen Russian-Western relations deteriorate.

"We are convinced that today, (the Ukraine crisis) cannot be solved by further escalation of the military scenario without taking into account vital interests of the southeastern regions of the country and without a peaceful dialogue with its representatives," Putin said.

He added that Russia could stand to lose as much as 100 billion rubles -- $2.8 billion -- if goods from Ukraine's trade deal with the EU were to reach the market. If that deal hurt Russia's bottom line, Putin said his country would retaliate.

Poroshenko said the situation at the Russian-Ukrainian border is unfavorable and reiterated his desire to regain control.

"The prime condition for a stabilization of the situation in Donbass is the establishment of effective control over the Russian-Ukrainian border," Poroshenko said. "It is vital to do everything to stop deliveries of equipment and arms to the fighters."

More than 2,000 people have been killed since the fighting began in April, but the Ukrainian army has now driven back the pro-Russian rebels in a recent offensive.