The 15 members of the Security Council hope to adopt the text on Friday when UN envoy Staffan de Mistura will report on efforts to silence the guns and revive peace talks.
Russia and the United States have set a deadline of midnight Damascus time (2200 GMT) Friday for the "cessation of hostilities" between President Bashar al-Assad's regime and non-jihadist rebel forces.
The deal -- which excludes the Islamic State (IS) group and other Sunni extremists -- marks the biggest diplomatic push yet to help end the five-year conflict in Syria which has claimed more than 270,000 lives and displaced more than half of the population.
"We are very cautious about raising expectations on this," Obama said in the Oval Office, where he was hosting Jordan's King Abdullah II.
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"The situation on the ground is difficult" he said. "But we have seen modest progress over the course of the last week or so with respect to humanitarian access to populations that are threatened."
Russia and the United States are on opposing sides of the conflict, with Moscow backing Assad and Washington supporting the opposition, but the two powers have been making a concerted push for the ceasefire to be respected.
The Kremlin said Assad had assured President Vladimir Putin of "the readiness of the Syrian government to facilitate the establishment of a ceasefire".
Putin and Assad also "stressed the importance of continuing an uncompromising fight" against IS, Al-Nusra Front and "other terrorist groups," the Kremlin said.
The agreement allows military action to continue against IS, which seized control of large parts of Syria and Iraq in 2014, the Al-Qaeda affiliated Al-Nusra and other jihadist groups.
The Russian defence ministry said it was in talks with rebel groups in five Syrian provinces -- Hama, Homs, Latakia, Damascus and Daraa -- on implementing the deal.
The Kremlin said Putin also discussed the deal with the leaders of Saudi Arabia and Iran.