The development came after Hezbollah fired rockets and launched drones early on Monday toward northern Israel.
Israel retaliated with a wave of airstrikes that killed 50 people in Lebanon, including seven children as well as a Palestinian militant and a Hezbollah intelligence official in Beirut's southern suburbs.
That death toll is a revised figure from an earlier one reported by the Health Ministry, which originally said 52 people had died in the strikes. Lebanese Health Minister Rakan Nassereddine then on Tuesday reduced that number to 40, then later raised the toll to 50.
Lebanon also said 335 people were wounded and that tens of thousands were displaced.
The UN refugee agency said 30,000 displaced people were staying in collective shelters in Lebanon, "while many others slept in their cars, on sides of the roads as they could not yet find safe shelter".
Hezbollah fired two salvos of rockets toward northern Israel, the militant group said while Israeli airstrikes overnight damaged a building housing Hezbollah's television and radio stations.
Beirut's southern suburbs also saw a series of strikes on Tuesday afternoon that came without warning. The Israeli military later said it targeted Hezbollah officials.
The Israeli military's Arabic spokesman, Avichay Adraee, warned residents of more than 80 villages and towns in southern Lebanon to leave, adding that people should not return to these areas until further notice.
A senior Hezbollah official said the group has no option but to fight Israel.
"The Zionist enemy wanted an open war, which it has not stopped since the ceasefire agreement," Mohamoud Komati said.
"So let it be an open war," he said.
Lebanese President Joseph Aoun told the ambassadors of Saudi Arabia, Qatar, the United States, France and Egypt that Hezbollah has been firing rockets from areas north of the Litani River.
The Israeli military said it sent additional troops into southern Lebanon and took new positions on several strategic points close to the border. Lebanon's state-run National News Agency said the Lebanese army was evacuating some of its positions along the border.
Adraee, the Israeli spokesman, said on X that the troops' movements inside Lebanon are meant to bolster Israel's forward defence system and create an addition layer of security.
Lebanon's state-run National News Agency said the Lebanese army was evacuating some of its border positions.
A Lebanese military official said Israeli troops had moved into southern Lebanon and the Lebanese army was "repositioning" in the area.
Thousands of Syrians living in Lebanon have crossed back into Syria, fleeing Israeli strikes over the past two days.
UNHCR said the number of people crossing from Lebanon into Syria jumped on Monday to 10,629 from typically between 3900 and 4400 a day since the holy Islamic month of Ramadan began in February.