Obama Thursday spoke to German Chancellor Angela Merkel over the phone about the situation in Ukraine, as Kiev and the West accused Russia of launching a new incursion into the country's east, Xinhua reported.
"We agree, if there was ever any doubt, that Russia is responsible for the violence in eastern Ukraine," Obama said.
"The violence is encouraged by Russia. The separatists are trained by Russia. They are armed by Russia. They are funded by Russia."
"And this ongoing Russian incursion into Ukraine will only bring more costs and consequences for Russia," Obama added.
Russia denied sending weapons and soldiers to help the rebels, saying the men captured Monday had crossed an unmarked section of the border by accident.
Kiev announced that Russian forces seized the port of Novoazovsk and several towns and villages in the Donetsk region.
The North Atlantic Treaty Organisation (NATO) said more than 1,000 Russian troops were believed to be operating inside Ukraine.
"Throughout this process, we've seen deep Russian involvement in everything that they've done," Obama said.
"I think in part because of the progress that you had seen by the Ukrainians around Donetsk and Luhansk, Russia is determined that it has to be a little more overt in what it had already been doing, but it's not really a shift."
According to Obama, a NATO summit scheduled for September in Britain would focus on "additional steps" to ensure the alliance's preparedness for "any challenge", and that he would reaffirm the "unwavering" US commitment to Ukraine when he meets with President Petro Poroshenko next month at the White House.
Obama once again ruled out a military solution to the Ukrainian crisis.