An Israeli cluster bomb exploded in the southern village of Ansar on Monday, killing one person and wounding six, Lebanese police said.
Six people were also wounded, including a rescue worker, when another cluster bomb exploded in the Nabatiyeh area.
In a joint statement, the UN and the Lebanese government “urged the population to exercise extreme caution, due to the large quantities of unexploded artillery and mortar shells strewn across the countryside”.
The UN’s ceasefire resolution that was agreed on Saturday, calls on Israel to provide “all remaining maps of land mines in Lebanon in Israel’s possession”.
Israel laid more than 400,000 mines during its previous occupation of south Lebanon from 1978 to 2000.
The warning came as thousands of Lebanese headed home after the ceasefire began at 05:00 GMT (8am local time).
Huge traffic jams clogged roads leading out of the main port cities of Tyre and Sidon, as cars and pick-ups loaded with families and their belongings headed eastwards to their villages in the mountains.
Tractors tipped earth on bombed roads to open areas in the south which had suffered massive damage from Israeli air strikes.
Imad Ibrahim began his journey at exactly 8am and headed to his home village of Dweir.
“I am going alone to inspect our house in the village and see if this ceasefire stands. If all is fine, I will return to Sidon to bring back my family,” he said.
Aid also began moving back towards southern Lebanon and the UN’s World Food Programme said it sent 24 trucks of food and medicine towards Tyre from Beirut.
The Israeli army said it was maintaining a ban on unauthorised traffic in parts of south Lebanon, saying that it remained in force to prevent the movement of Hezbollah fighters, and that any vehicles on the roads risked attack.