Ukrainian President Petro Poroshenko came out in support of an aid mission but made clear it had to be an international effort under the backing and protection of the International Community of Red Cross, involving the European Union as well as Russia, according to The Associated Press.
The White House quoted Obama as saying that any Russian intervention without the Ukrainian government's agreement would be "unacceptable" and a violation of international law, the AP reported.
Earlier, Kiev said it was in the "final stages" of recapturing the eastern city of Donetsk, the main base of the separatist rebels, in a battle that could mark a turning point in a conflict that has caused the biggest confrontation between Russia and the West since the Cold War, according to the AP.
The Noth Atlantic Treay Organization Secretary-General Anders Fogh Rasmussen said there was no sign Russia had withdrawn the troops it had massed at the Ukrainian frontier, and said "there is a high probability" Russia would use the troops to intervene, the AP reported.
"We see the Russians developing the narrative and the pretext for such an operation under the guise of a humanitarian operation, and we see a military build-up that could be used to conduct such illegal military operations in Ukraine," Rasmussen said, according to the AP.
Russia has massed 45,000 troops on its border, NATO said there was a "high probability" that Moscow could intervene militarily in the country's east, where Kiev's forces are closing in on pro-Russian separatists, the AP reported.
Western countries believe that Putin could now send his forces into the east to head off a humiliating rebel defeat, according to the AP.
European Commission President Jose Manuel Barroso delivered a blunter message directly to Putin in a telephone call on Monday, the AP reported. "President Barroso warned against any unilateral military actions in Ukraine, under any pretext, including humanitarian," the Commission said in a statement.