He warned Russia that all parties to the cessation of hostilities needed to stop attacks, including air strikes, the BBC wrote.
If successful, he said, the truce could be a first step towards ending the chaos and violence in Syria.
And he vowed to defeat the so-called Islamic State (IS), which he said was "not a caliphate but a crime ring."
Obama said the success of the cessation of hostilities would depend on whether parties including the Syrian government, Russia and their allies lived up to their commitments.
Attacks needed to end and humanitarian aid had to be allowed through to desperate civilians, he said.
"The coming days will be critical and the world will be watching," he said.
Earlier, Russian Foreign Minister Sergey Lavrov said he hoped the U.S. would respect the truce.
Obama said that factional rivalry among the rebels, as well as the campaign against IS, meant there would be no immediate end to violence.
He also insisted that Syrian President Bashar al-Assad had to step down from power as part of any solution to Syria's civil war, but acknowledged there was "significant dispute" with Russia and its allies over this point.
"It is clear that after years of barbarity against his people, many will not stop fighting until Assad is out of power," he said.
Obama also said progress was being made in the fight against IS, but added that the only way to inflict a lasting defeat on the group was to bring an end to the Syrian conflict.
