A partial cease-fire brokered by U.S. President Donald Trump failed to stop fighting between Israel and Hezbollah in southern Lebanon and across the Israeli border. Photo by Atef Safadi/EPA

June 2 (UPI) -- Israel and Hezbollah continued to exchange fire on Tuesday, a day after U.S. President Donald Trump intervened to broker a partial cease-fire he said both sides had signed onto.

At least four municipalities in and around the southern Lebanese city of Nabtieh, 15 miles southeast of Sidon, were targeted by Israeli strikes, injuring two Lebanese Army soldiers and an Israeli drone had overflown Beirut at low altitude, according to Lebanese media.

Lebanon's National News Agency said the Israeli military had reiterated evacuation orders to the Nabatieh residents, telling them to head north of the Zahrani River and said several other areas of southern Lebanon had been struck, including Debbine, where a "very violent" blast from a large-scale demolition by Israeli forces had shaken the town.

The Israeli military said in a post on X that air raid warnings were activated just before 2 a.m. local time by "the intrusion of hostile aircraft into several areas in the north of the country" and that it had intercepted two projectiles that had been fired into northern Israel from Lebanon.