The Israeli military said early Tuesday that troops have started "ground raids" in villages in southern Lebanon, after militant group Hezbollah said it had targeted "enemy soldiers" at the countries' border.
A Lebanese security official said Israeli Defense Forces (IDF) had also conducted at least six strikes on south Beirut after Israel's army ordered residents in the Hezbollah stronghold to evacuate.
Despite international calls for de-escalation, Israel earlier vowed to keep fighting Hezbollah and sealed part of the border after killing the Iran-backed group's leader.
Israeli Defense Minister Yoav Gallant warned the battle was not over even after the massive strike on Beirut that killed Hezbollah chief Hassan Nasrallah on Friday, dealing the group a seismic blow.
The military said troops backed by airstrikes and artillery launched ground raids "a few hours ago" targeting militant group Hezbollah "in villages close to the border".
Israel informed its main weapons supplier Washington of the incursions, US State Department spokesman Matthew Miller told journalists.
US President Joe Biden earlier on Monday indicated he opposed an Israeli ground operation. The US is sending more troops to the region.
"We should have a ceasefire now," he said.
Hezbollah fighters were "ready if Israel decides to enter by land", the group's deputy leader Naim Qassem said in a first televised address since Nasrallah's death.
In a statement, Hezbollah said it "targeted" Israeli troops carrying out "movements" in orchards near the border, with a source close to the group saying the soldiers were "right on the border".
There was no immediate comment from Hezbollah following the Israeli army's announcement of the ground raids, but the group's al-Manar television reported the Israeli statement announcing the raids on its Telegram channel.
Lebanon's national army, dwarfed by Hezbollah's military power, was "repositioning" troops farther from the border, a military official told AFP.
World leaders have urged de-escalation, with United Nations Secretary-General Antonio Guterres's spokesman Stephane Dujarric saying: "We do not want any sort of ground invasion."