Censor.NET reports citing The Financial Times.
Mr. Obama said Saturday's attack by separatist rebels on the southeastern Ukrainian city of Mariupol was clearly backed, equipped and financed by Russia, according to journalists Roman Olearchyk and Victor Mallet.
Mr Obama's statement, made on Sunday at a news conference in New Delhi with Indian Prime Minister Narendra Modi, came as Ukrainian President Petro Poroshenko met his security council in Kyiv and urged the international community to increase pressure on Russia.
Mr Obama said the U.S. was "deeply concerned" about the latest break in the ceasefire and the separatists had received "Russian backing, Russian equipment, Russian financing, Russian training and Russian troops".
He added: "I will look at all additional options that are available to us short of military confrontation and try to address this issue."
Despite the strong rhetoric from the White House, it was unclear whether the EU - the Obama administration's most important ally on Russia policy - was prepared to follow suit.
According to EU diplomats, capitals were divided over whether to pursue more sanctions. Federica Mogherini, the high representative, has called an emergency meeting of foreign ministers for Thursday.
Some diplomats had balked at the idea of convening an earlier meeting for fear it would result in little more than a further condemnation of the Mariupol attack. "To call it just to adopt another statement makes no sense," said a Polish diplomat.
Among those reluctant to call a quick meeting without "deliverables" was Donald Tusk, the European Council president, who said on Twitter that Mariupol showed that "appeasement encourages the aggressor".
Still, the feverish diplomacy over whether to move towards new sanctions reflected a shift in tenor for the west, particularly in Europe, where some leaders had started the year openly discussing lifting sanctions on Russia because of the crumbling Russian economy, which had been brought low by tumbling oil prices and value of the rouble.
"We have no interest in seeing Russia weakened or its economy in a shambles," Mr Obama said. "We have a profound interest, as I believe every country does, in promoting a core principle, which is: large countries don't bully smaller countries, they don't encroach on their territorial integrity, they don't encroach on their sovereignty. And that's what's at stake in Ukraine."
The attack came a day after a senior separatist leader ruled out further ceasefire talks and vowed to recapture additional cities in Ukraine's industrial east. The escalated fighting along the entire perimeter of separatist-held territory in past weeks threatens to plunge the 10-month conflict that has claimed more than 5,000 lives back into full-scale warfare.
On Sunday, Russia showed no sign of backing down. In statements put out by the Kremlin after Sergei Lavrov, the foreign minister, spoke with his US and EU counterparts, Moscow pinned blame for the heightened violence on Kyiv for refusing to engage directly with separatist leadership.
The Russian foreign ministry accused Kyiv of violating the September Minsk ceasefire agreements and of pursuing a "course towards further militarisation".
In addition to Mr Obama publicly citing Russian involvement in the Mariupol attack, security chiefs in Kyiv claimed to hold evidence implicating Russian operatives in the rocket fusillade.