He predicted that al-Assad would keep some of his chemical weapons arsenal, and "then use it against our people and the FSA and then he will come out and accuse terrorists, and he will say that he gave up everything he has."
The Syrian government refers to the opposition fighters as terrorists and has previously accused them of chemical weapons use.
Some inside Syria criticized the focus on chemical weapons. Protesters in one town held up a banner in Arabic saying they are "worried that the international community is giving Assad a license to kill with all kinds of weapons except the use of chemical weapons."
Hopes for peace
French Foreign Minister Laurent Fabius said the U.S.-Russian agreement "constitutes an important step forward," a sentiment echoed by UK Foreign Secretary William Hague.
The two plan to meet Kerry on Monday in Paris to discuss the framework and its implementation.
Ban pledged U.N. support for the plan, his spokesman said, and expressed hope that it would both prevent any future use of chemical weapons and pave the way for a political solution in Syria.
Kerry and Lavrov announced the deal on their third day of talks.
Friday, they signaled their intent to meet later this month on the sidelines of the U.N. General Assembly in New York, where they hope to set a date to restart long-stalled parallel talks on the broader issue of ending the Syrian civil war.
The U.N. estimates more than 100,000 people have been killed since the civil war began in 2011, in addition to more than 2 million becoming refugees and over 4 million being displaced within Syria.