Israel's military says it has carried out fresh strikes on southern Lebanon, targeting what it called Hezbollah infrastructure.
Social media videos from Tyre, one of Lebanon's biggest cities, show dust-covered crowds of people gathered around collapsed buildings.
On Wednesday, the Israel Defense Forces (IDF) had urged residents to move north of the Zahrani River, about 40km (25 miles) from the border. The IDF said it would act "with extreme force", accusing Hezbollah of repeated ceasefire violations.
Hezbollah, which has accused Israel of violating the ceasefire, said its fighters had clashed with Israeli troops on Wednesday.
Two sets of Israeli strikes hit Tyre - causing a building fire - and an area to the city's east on Thursday morning, Lebanon's state-run National News Agency (NNA) reported.
Wednesday's evacuation order was the largest since the ceasefire took effect on 17 April, covering about 14% of Lebanese territory.
The strikes came after Israeli Prime Minister Benjamin Netanyahu announced an expansion of its ground operation following Hezbollah drone attacks on troops occupying part of southern Lebanon and on civilians in northern Israel.
Wednesday's order for Tyre was swiftly followed by air strikes. Residents watched with horror from balconies, filming on their phones, as Israeli forces hit the city.
Rida, 52, owned a cafe near the beach that was destroyed alongside his home in an air strike minutes before the ceasefire started last month. He previously told the BBC he would never leave Tyre.
Now, the feeling is different. "I went to the port next to the beach and a lot of people are there," Rida said over the phone on Wednesday. "People packed up their stuff. Everyone is scared."
The later evacuation order for areas south of the Zahrani River covers about 300 towns and villages. Many residents, including those already displaced from other parts of southern Lebanon, have nowhere obvious to go.
The head of the International Committee of the Red Cross (ICRC) delegation in Lebanon warned the situation in the country's south was "nearing a perilous tipping point".
"Ongoing hostilities create conditions that are untenable for civilians and risk long-term consequences," said Agnes Dhur.
Officials and humanitarian workers said Sidon, a coastal city south of the capital Beirut, could no longer absorb the growing influx of displaced families. They urged civilians to relocate to the Beqaa Valley and Mount Lebanon further east.
Also on Wednesday, Lebanese media reported a wave of Israeli strikes across the south and the eastern Bekaa Valley, with four people killed in the towns of Choukine and Nabatieh.
Hezbollah said on Wednesday that its fighters had clashed with Israeli forces "at point-blank range" in Zawtar al-Sharqiyeh, north of the Litani River. The town, about 30km (19 miles) from the border, lies outside the Israeli-declared "buffer zone".
Israeli officials have said Hezbollah's attacks are violating the temporary ceasefire deal between the Israeli and Lebanese governments, which has been extended twice since it came into force last month.
Lebanese officials have pointed to the Israeli strikes themselves as violations.
The escalation threatens to derail talks aimed at ending the war between the US, Israel and Iran. Iran insists that any deal must also cover Lebanon. Israel says it reserves the right to continue to fight the threat from Hezbollah.
Lebanon was drawn into the war on 2 March, when Hezbollah launched rockets into Israel in retaliation for an Israeli strike that killed Iran's supreme leader. Israel responded with an air campaign across Lebanon and a ground invasion.
At least 3,213 people have been killed in Lebanon since the start of the war, according to the country's health ministry - its figures do not distinguish between combatants and civilians.
Israel says 23 of its soldiers and four Israeli civilians have been killed over the same period on both sides of the border.
Additional reporting by Angie Mrad
