"What is required is the handover of the bodies of the resistance fighters who fell as martyrs during the latest confrontations in order to defuse the tension on Lebanon's international border," Prime Minister Fuad Saniora told reporters during a visit to Qatar on Wednesday.
A Lebanese cabinet minister close to Hizb Allah reiterated the demand on Thursday, warning Israel that unless the bodies were returned, the militant group might try to kidnap Israelis to trade them for the bodies.
"They must be handed over in order to avoid an escalation," Health Minister Mohammed Jawad Khalife of the Amal Party told Voice of Lebanon radio.
"It is known that the resistance will try to secure the return of the bodies one way or another, and this usually ends up in negotiations to trade them for the bodies of Israeli soldiers or for prisoners."
In Israel, there was no immediate response to the Lebanese demand.
Four guerrillas were killed and 11 Israeli soldiers were wounded in Monday's fighting on the south Lebanon border.
Israeli warplanes and artillery bombarded Hizb Allah positions, and the guerrillas fired missiles at Israeli military outposts.
Pamphlet drop condemned
Of the four guerrillas, three were killed when they crossed over the Israeli border, and a fourth wounded guerrilla, who was retrieved by his comrades, later died on the Lebanese side.
"It is known that the resistance will try to secure the return of the bodies one way or another, and this usually ends up in negotiations to trade them for the bodies of Israeli soldiers or for prisoners"
Mohammed Jawad Khalife.
Lebanon's health minister
Lebanese security officials, speaking on condition of anonymity because of the sensitivity of the issue, said the government had passed the request for the bodies to the UN peacekeeping force on the border, which mediates between the two states that are technically at war. UN officials had no immediate comment.
Fighting briefly resumed on Wednesday when an Israeli civilian in a hang glider drifted across the border and landed inside Lebanon. Israeli troops shot at Hizb Allah guerrillas to prevent them from capturing the civilian as he ran back to Israel.
Earlier on Wednesday, Israeli planes dropped thousands of anti-Hizb Allah leaflets over Beirut and other Lebanese regions.
In Qatar, Prime Minister Saniora said he condemned the pamphlet drop as yet another example of Israeli violation of Lebanese territory, according to a report by Lebanon's official National News Agency.
Lebanon has repeatedly complained of Israeli overflights, which have been censured by the United Nations.
The Lebanese Cabinet was expected to discuss this week's border clashes at a meeting later on Thursday.
Appeal for restraint
The UN Security Council accused Hizb Allah on Wednesday of starting this week's attacks. In a statement, the council appealed for restraint from both sides.
Prime Minister Saniora condemned
Israel's pamphlet dropping
Hizb Allah has denied initiating the attacks. A close ally of Syria, it is thought the group was trying both to capture Israeli soldiers for a future exchange of prisoners and to take pressure off Damascus.
Last year, Hizb Allah swapped an Israeli businessman and the bodies of three Israeli soldiers for about 400 Palestinian and Lebanese prisoners.
An escalation of tension in southern Lebanon could strengthen Syria's hand with the United Nations by underlining the need for Syrian influence in maintaining peace in the region.
A UN investigation into the February assassination of former Lebanese Premier Rafik Hariri has implicated Syrian intelligence. But Damascus and the UN investigators have failed to agree on a venue for the questioning of six Syrian officials. The UN Security Council warned Syria this month that it must cooperate fully with the investigation or face further action.