Smoke plumes billow during ongoing battles in the southern Gaza Strip on Tuesday. AFP

Israeli strikes on Tuesday killed at least 13 people in central Gaza, the civil defence agency in the Hamas-run territory said, although fighting has largely subsided as Muslims mark Eid Al Adha.

An Israeli announcement at the weekend of a daily "pause" of military activity to facilitate aid flows coincided with the Muslim holiday and has brought relative calm to parts of the besieged Gaza Strip after more than eight months of war.

But despite the rare lull in Gaza, tensions surged around Israel's northern border with Lebanon, as Foreign Minister Israel Katz warned of Hezbollah's destruction in a "total war".

In central Gaza, witnesses reported gunfire and artillery shelling near the Nuseirat refugee camp, where the civil defence agency said at least 13 people were killed in two separate strikes on a family home and a commercial building.

Al-Awda hospital said it received the bodies of "six martyrs and 15 wounded as a result of Israeli air strikes on various areas in the central and southern Gaza Strip".

Witnesses and the Hamas government media office said there were some strikes and fighting elsewhere in northern and central Gaza.

Israeli military vehicles maneuver inside the Gaza Strip as seen from Israel on Tuesday. Reuters

In a statement, the Israeli army said its operations continued Tuesday in central and southern Gaza including Rafah city on the border with Egypt.

"We've been taking apart Hamas in Rafah for the last month," said military spokesman David Mencer.

"Terror outposts in Shaboura and Tal al-Sultan are being defeated. We've eliminated hundreds of terrorists," he said, adding "an Islamic Jihad sniper cell (was) eliminated".

Mounting criticism

Amid mounting criticism over his handling of the hostage crisis, Israeli Prime Minister Benjamin Netanyahu invited the relatives of killed hostages to his home, several families told AFP Tuesday.

But one relative, who spoke on condition of anonymity, said she would decline the invitation, saying, "he remembered a little late to invite us".

In Jerusalem on Monday, thousands of Israelis protested against Netanyahu's government over its failure to negotiate the release of scores of hostages held in the Palestinian territory since Hamas's October 7 attack.

Demonstrators rallied outside the parliament and near Netanyahu's residence, demanding early elections and chanting "All of them! Now!", referring to the release of hostages.

"We need to shut down the country in order to make the government fall," said Yaacov Godo, whose son Tom was killed during the Hamas attack, at the start of what activists describe as a week of anti-government action across the country.

Israeli media said another rally was planned in front of the parliament building late Tuesday.