Updated

The president of the U.N. Security Council says many members are pressing to follow up on last week's resolution to eliminate Syria's chemical weapons with a demand that President Bashar Assad's government allow immediate access to the country for desperately needed humanitarian aid.

Australian Ambassador and council president Gary Quinlan said Monday the draft statement calls for delivering access in "the most effective ways, including across conflict lines and, where appropriate, across borders from neighboring countries ..." if necessary to bypass meddling from Assad's regime in Damascus.

Council members are striving to adopt the statement by Wednesday or Thursday.

Quinlan says he sees "strong unanimity" to quickly adopt a non-binding statement rather than spend weeks trying to pass an enforceable resolution.