The Israeli military says Hezbollah has fired into a disputed border zone, the group's first attack since a ceasefire took hold last week.

Israel and Hezbollah exchanged air strikes and rocket fire on Monday as their 60-day ceasefire appeared to be unravelling within its first week.

The Israeli military said on Monday it struck dozens of targets throughout Lebanon, shortly after Hezbollah accused Israel of violating a ceasefire agreement and fired missiles on an Israeli military position in the disputed Shebaa Farms area.