A fresh Israeli air attack in the south and shelling across the frontier on Tuesday followed the previous day's bloody clashes in which four Hizb Allah fighters were killed and 11 Israeli soldiers wounded.
Israeli Defence Minister Shaul Mofaz said the attacks in the past 24 hours were the fiercest by both sides since Israeli troops quit south Lebanon after 22 years' occupation, a withdrawal claimed as victory by Hizb Allah.
Meanwhile, Lebanese President Emile Lahoud, under pressure since Syria pulled out its troops from Lebanon in April, sat in frosty silence next to his rival, Prime Minister Fuad Siniora, at an Independence Day military parade.
In a gesture towards Damascus, he said Beirut wanted good relations with its large neighbour, which had been active in Lebanon since its troops were sent to the country in 1976 after a resolution at an Arab summit in Cairo.
But it depends on Syria, Siniora said. "We want to have excellent relations with Syria, based on mutual respect."
He added: "The problem is not on the side of Lebanon, which unceasingly expresses its stand for ties based on cooperation and mutual respect."
Relations between Damascus and Beirut deteriorated dramatically after the murder of former Lebanese premier Rafiq al-Hariri in February and led to the pullout of Syrian forces two months later.
Earlier on Tuesday, Israeli artillery shelled a Hizb Allah post in the divided village of al-Ghajar (Gypsies in English), said an AFP correspondent. There was no immediate word on casualties.
Part of al-Ghajar lies on Lebanese territory and part in the occupied Golan Heights, a strategic plateau which Israel seized from Syria in 1967.
In Jerusalem, an Israeli military spokesman said: "This attack targeted a position used by Hizb Allah to fire rockets and mortar shells at the north of Israel."
On Tuesday, Israeli artillery
shelled a Hizb Allah post
Hizb Allah forces were on high alert in the disputed Shebaa Farms district, where Monday's clashes took place. The area was captured by Israel from Syria at the same time as the Golan but is now claimed by Beirut.
Siniora blamed Israel for the latest clashes, saying that Israeli aircraft "have never stopped violating Lebanese airspace in the past weeks", fuelling tension at the frontier.
An official with the UN peacekeeping force said that the situation in the southern frontier zone remained "very tense and dangerous".
The Islamic Resistance (the armed wing of Hizb Allah) on its website accused the Israelis of entering al-Ghajar village, prompting Hizb Allah fighters to respond.
The website said its fighters inflicted deaths among the Israeli attacking force.
Chants of "Death to Israel, Death to America" rang through village Zibqin as thousands of Hizb Allah supporters attended the funeral of Yussef Ali Barak, one of the four fighters killed on Monday.
"Islamic Resistance has given one of the most beautiful pictures of defending Lebanon's sovereignty and independence against Israel," Shaikh Nabil Qauq, the local Hizb Allah official in the south, told mourners.
"We are determined to free Shebaa Farms and release the prisoners held in Israeli prisons," he added.