Bolton says he believes it is likely to be adopted in the next few days.
The Associated Press quoted an official with knowledge of the talks as saying the draft calls for a "full cessation of violence" between Israel and Hizballah, but would allow Israel the right to launch strikes if Hizballah attacks it.
The resolution reportedly does not call for an "immediate cessation of violence." That's seen as a victory for the United States and Israel.
France and many other nations had demanded an immediate halt to violence without conditions as a way to push the region back toward stability.
(AP, Reuters, dpa)
Iranians demonstrating in support of Hizballah in Tehran on July 17 (epa)
'FOR THE SAKE OF LEBANON': The Islamic Republic of Iran has served as an ideological inspiration for Hizballah since the Lebanese militant group's creation in 1982, and Tehran acknowledges that it supports the organization morally and politically. "Yes, we are friends of Syria and Iran" Hizballah leader Hassan Nasrallah has said. "For 24 years we benefited from our friendship with Syria and Iran for the sake of Lebanon...." (more)