The military's announcement followed Prime Minister Benjamin Netanyahu's pledge to keep fighting a "sacred war" until Israel's enemies -- Hezbollah and Hamas -- are defeated. Both groups have vowed no let-up in the multi-front conflict.
Israel expanded its military operations in Lebanon last month after Hezbollah opened a front in support of its Palestinian ally Hamas, following the deadliest attack in its history on October 7, 2023.
While battling Hamas in Gaza, Israel has also focused on securing its northern border to allow tens of thousands of displaced Israelis to return home.
Israel launched a wave of strikes against Hezbollah strongholds in Lebanon on September 23, leaving at least 1,110 people dead since then and forcing more than a million people to flee their homes.
Israeli operations have for the most part focused on areas in the south and east of Lebanon, traditional strongholds of Hezbollah, as well as the Iran-backed group's main bastion in south Beirut.
While areas along the southern coast have not been spared, Israel's latest evacuation warning to residents suggested a further expansion of the conflict northwards along the coastline.
On its Telegram channel, the Israeli military said its 146th Division began "limited, localised, targeted operational activities" against Hezbollah targets and infrastructure in southwestern Lebanon.
The military had on Monday said it would expand its operations against Hezbollah to south Lebanon's coastal area and warned people to stay away from the shore.
The army "will soon operate in the maritime area against Hezbollah's terrorist activities" south of the Al-Awali river, army spokesman Avichay Adraee wrote on social media.
On Tuesday, he reiterated the call to residents of south Lebanon not to return home.
Hezbollah said it had fired a salvo of rockets at Israeli troops in two areas of northern Israel.
The intensity of Israeli strikes on southern Beirut, which has been repeatedly pounded even after a bombing killed Hezbollah's leader Hassan Nasrallah, decreased somewhat overnight, AFP correspondents said.
The official National News Agency said more strikes hit southern and eastern Lebanon.
'War of attrition'
The expansion in the fighting in Lebanon came a day after Israelis and people around the world marked a year since Hamas's October 7 attack on Israel.
For families of the bereaved, as well as relatives of 251 people taken hostage into Gaza, the pain was especially acute.
Of the total number, 97 hostages are still being held, including 34 the Israeli military says are dead.
Hamas's October 7 attack resulted in the deaths of 1,206 people, mostly civilians, according to an AFP tally based on official Israeli figures, which include hostages killed in captivity.
The attack sparked Gaza's deadliest-ever war, which according to the health ministry in the Hamas-run territory has killed 41,909 people, also mostly civilians. The UN has said the figures are reliable.
It has since expanded into Lebanon, with Israeli troops battling Hezbollah, while other Iran-backed groups in the region including Yemen's Huthis have also stepped in.
As Iran awaits what Israel has said will be retaliation for an Iranian missile barrage last week, Tehran hailed the October 7 attack.
In a pre-recorded television address, Netanyahu vowed not to give up on the "sacred mission" of achieving the war's goals.
"As long as the enemy threatens our existence and the peace of our country, we will continue to fight. As long as our hostages are still in Gaza, we will continue to fight," said the Israeli leader.
Weakened but not crushed after a year of war, Hamas was defiant, with Abu Obeida, spokesman for Hamas's armed wing, saying the group would "keep up the fight in a long war of attrition, one that is painful and costly for the enemy".
He also said scores of people taken hostage into Gaza last year were enduring a "very difficult" situation.
'No rehabilitation'
A senior Hamas official has acknowledged "several thousand fighters from the movement and other resistance groups died in combat".
When the Gaza war began, Netanyahu vowed to "crush" Hamas, but troops have found themselves returning again to areas to confront signs the movement was trying to rebuild.
Netanyahu has vowed to bring home the hostages, but critics in Israel have accused him of obstructing mediation for a truce and hostage-release deal.
Vigils at massacre sites and rallies called for the return of hostages a year after their abduction.
Late Monday in Tel Aviv, musicians performed as victims' images flashed on screens at a ceremony attended by families and relatives of those killed and abducted.
"We know in our minds, our hearts, in every cell in our bodies: there will be no rehabilitation without the return of the hostages. All of them," said Nitza Corngold, whose son Tal Shoham was kidnapped.
'Graveyard'
A year since the start of Israel's military offensive in Gaza, swathes of the territory have been reduced to rubble, and nearly all its 2.4 million residents have been displaced at least once.
Philippe Lazzarini, head of the UN agency for Palestinian refugees, UNRWA, said on X Monday the war had turned Gaza into a "graveyard".
Israel's military says 350 soldiers have been killed since the Gaza ground offensive began on October 27.
People in Gaza just want the war to end.
"I have grown old while watching my children hungry, scared, having nightmares and screaming day and night from the sound of the bombing and shells," said one displaced woman, Israa Abu Matar, 26.
burs/ser/dv
