The bloodshed, which one analyst said was unlikely to re-spark war between Israel and Iran-backed Hezbollah, came hours after the extension of a Sunday deadline for Israeli forces to withdraw from south Lebanon under a November ceasefire deal.
The ministry said Israeli fire killed 24 returnees on Sunday.
"Israeli enemy attacks as citizens attempt to return to their towns that are still occupied have led... to two dead and 17 wounded," the health ministry said Monday in a statement, updating an earlier toll of one dead.
It said the wounded included a child and a rescuer from the Risala Scouts association, affiliated with Hezbollah ally the Amal movement.
Under the ceasefire deal that took effect on November 27, the Lebanese military was to deploy in the south alongside United Nations peacekeepers as the Israeli army withdrew over a 60-day period, which ended on Sunday.
Hezbollah was also to pull back its forces north of the Litani River -- about 30 kilometres (20 miles) from the border and dismantle any remaining military infrastructure in the south.
Caretaker Prime Minister Najib Mikati said earlier Monday that Lebanon had agreed to an extension of the ceasefire deal between Hezbollah and Israel until February 18, after the Israeli military missed Sunday's deadline to withdraw.
In south Lebanon, residents accompanied by the army were again trying to return to their villages, official media and AFP correspondents reported.
In the village of Burj al-Muluk, an AFP photographer saw dozens of men, women and children gathering in the morning behind a dirt barrier, some holding yellow Hezbollah flags, hoping to reach the border town of Kfar Kila, where the Israeli military is still deployed.
- 'Bullets don't scare us' -
In the city of Bint Jbeil, an access point for many border villages, Hezbollah supporters distributed sweets, water and images of former chief Hassan Nasrallah, who an Israeli air strike killed in September.
Others handed out stickers celebrating the "victory from God" as women held pictures of slain Hezbollah fighters.
"They think they are scaring us with their bullets, but we lived under the bombing and bullets don't scare us," said Mona Bazzi in Bint Jbeil.
The official National News Agency (NNA) said Lebanese "army reinforcements" had arrived near the border town of Mais al-Jabal, where people had started to gather at "the entrance of the town" in preparation for entering alongside the military.
It said the Israeli army had "opened fire in the direction of the Lebanese army" near the town, without reporting casualties there.
"We waited in a long line for hours, but couldn't enter," said Mohammed Choukeir, 33, from Mais al-Jabal, adding that Israeli troops "were opening fire from time to time on civilians gathered at the entrance of the town".
In nearby Hula, the NNA said residents entered "after the deployment of the army in several neighbourhoods".
The truce has been marked by accusations of violations from both sides. It came after more than a year of hostilities between Israel and Hezbollah, including two months of all-out war.
- 'Israel must withdraw' -
A source close to Hezbollah told AFP that "seven fighters from Hezbollah were taken prisoner" by Israel before the truce, while four other people were apprehended by the Israeli military on Sunday in south Lebanon border villages.
In a televised speech later on Monday, Hezbollah leader Naim Qassem reiterated calls for the Israeli military to withdraw from the south.
"Israel must withdraw... any consequences of a delay in the withdrawal rests on the United Nations, the United States, France and the Israeli entity," Qassem said.
The US and France are part of a mechanism that deals with any violations of the ceasefire.
Qassem called for pressure on Israel to adhere to the original terms of the deal, hailing French President Emmanuel Macron's appeal before the latest extension.
Macron's office on Saturday said he had called on all parties to honour their commitment to the ceasefire as soon as possible.
Qassem warned that, "We are facing an occupation that is aggressive and refuses to withdraw, and the resistance has the right to act as it sees fit."
Hilal Khashan, professor of political science at the American University of Beirut, said he did not expect a return to major violence.
"Hezbollah no longer wants any further confrontation with Israel. Its goal is to protect its achievements in Lebanon," he told AFP.
Lebanon's army said Sunday that it had entered several border areas including Dhayra, Maroun al-Ras and Aita al-Shaab.
Israeli military spokesman Avichay Adraee on Monday called again for south Lebanon residents to "wait" before returning.
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