"We are in the face of a very big military victory," Sayyed Hassan Nasrallah said in a televised speech. The militants have "effectively lost" most of the land they held in the barren, mountainous border region of Jroud Arsal, he added.
As soon as the fighting ends, the Shi'ite Iranian-backed Hezbollah would be ready to hand over territory it has captured if the Lebanese army requests it, he said.
Hezbollah has made rapid advances since it launched an offensive with the Syrian army on Friday to drive Sunni militants from their last foothold along the frontier.