Thousands in southern Lebanon packed family members and belongings into cars, vans and trucks in a rushed attempt to evacuate their homes.
A Lebanese official coordinating the crisis response told Reuters news agency that 89 temporary shelters in schools and other facilities had been set up, with the capacity for more than 26,000 people as civilians fled.
In the southern port city of Sidon, cars heading north toward Beirut packed the main north-south highway linking the capital with southern communities.
The last time that Lebanon saw such a large wave of displacement was in 2006, when Israel clashed with Hezbollah, causing hundreds of thousands to flee their homes in the south.
On Monday, Israel warned residents in southern and eastern Lebanon to leave areas close to sites where Hezbollah is thought to be hiding weapons.
Lebanon officials say over 550 dead in strikes
Lebanon's health minister, Firass Abiad, said the death toll from Israeli strikes on the country's south had climbed to 558, including
50 children and 94 women.
Some 1,835 have been wounded, he added. Abiad said that emergency personnel were among the dead, with four paramedics among those killed and 16 paramedics and firefighters were among the wounded.
"The vast majority, if not all, of those killed in yesterday's attacks were unarmed people in their homes," Abiad said.
Hezbollah says rockets strike Israel explosives factory
Hezbollah said on Tuesday that it had attacked several Israeli military targets with rockets Tuesday morning, including an explosives factory 60 kilometers (37 miles) into Israel.
The militant group said it had attacked the explosives factory around 4 a.m. (0100 UTC) and the Megiddo airfield three separate times overnight.
Israel's military said that sirens warning of Hezbollah rocket fire sounded across northern Israel, including in the port city of Haifa, and in the northern part of the occupied West Bank, the military said.
Some 60,000 people have been evacuated from northern Israel as a result of the cross-border fighting.
Qatar suspends flights to Lebanon
Qatar Airways said on Tuesday that it had suspended flights to Beirut for the day as tensions escalated between Israel and Hezbollah.
"Due to the ongoing situation in Lebanon, Qatar Airways has temporarily suspended flights to and from Beirut Rafic Hariri International Airport until September 25," the Qatari national carrier said in a statement. "The safety of our passengers remains our highest priority."
Last week, Qatar Airways announced a ban on pagers and walkie-talkies on its Beirut flights following the communications device explosions that killed 37 people and wounded thousands over two days.
Lufthansa, Germany's national carrier, and Air France have also suspended or extended their suspension of flights to Beirut in recent days.