Lebanon's Hezbollah and Israel said they traded cross-border fire Sunday, as Israel fought the Shiite movement's ally Hamas on its southern flank a day after militants from the Palestinian group stormed its Gaza frontier.

Hezbollah and Hamas are Iran-backed Islamist groups that Israel and its allies consider terrorist organisations. Both have fought multiple wars with Israel in the past few decades.

Hezbollah said it carried out Sunday's assault "in solidarity" with a large-scale air, sea and land attack Hamas launched the day before against Israel, in a dramatic escalation of the Israel-Palestinian conflict.

"The Islamic resistance… attacked three positions of the Zionist enemy (Israel) in the occupied Lebanese Shebaa farms… with large numbers of artillery shells and guided missiles," the Shiite movement said in a statement.

Witnesses living on the Lebanese side of the border said a dozen rockets were fired towards Israel in the morning.

Israeli drones were seen overflying the frontier region by an AFP photographer.

The Israeli army said it launched artillery into southern Lebanon on Sunday in response to fire from the area.

"Israeli artillery is in the process of striking the area of Lebanon from which a shot was fired," the army said in a statement, without giving further details.

After launching its surprise assault on Israel at dawn on Saturday, the Palestinian Islamist group Hamas had called for "Arab and Islamic nations" to join the battle.

– 'We are ready' –

Lebanon's National News Agency said later two more rockets were fired from the Lebanese side towards enemy positions in the Shebaa farms, prompting Israel to retaliate with fresh artillery fire.

NNA said later that a baby and another child were injured by flying shards of glass caused by the Israeli strikes on Sunday.

Israel warned Hezbollah against being involved in the fighting.

"We recommend Hezbollah not to come into this. If they come, we are ready," army spokesman Richard Hecht told reporters.

The United Nations Interim Force in Lebanon (UNIFIL), which acts as a buffer between Lebanon and Israel, urged restraint.

"We are in contact with authorities on both sides… to contain the situation and avoid a more serious escalation," it said in a statement on Sunday.

There are 13 points of dispute along the so-called Blue Line, the frontier demarcated by the UN in 2000 after Israeli troops withdrew from southern Lebanon.

The Lebanese army said that starting Saturday it had deployed patrols at the border, adding it was "closely monitoring the situation in coordination with" UNIFIL.

In 2006 Hezbollah and Israel fought a 34-day war that left more than 1,200 dead in Lebanon, mostly civilians, and 160 in Israel, mostly soldiers. The two countries remain technically at war.

On Saturday, Hezbollah had praised Hamas for its "heroic operation" and said its leadership was following the developments and "in direct contact with the leadership of the Palestinian resistance at home and abroad".