Israel carried out an overnight raid inside Lebanon aimed at disrupting an arms transfer, the Israeli army says.
Lebanese troops have reached the southern border with Israel
One soldier died and two were injured in the Bekaa Valley operation, it said. Lebanese sources earlier told Reuters agency that three militants also died.
The incident came hours after UN chief Kofi Annan warned of a "fragile" situation on the ground.
Meanwhile, 50 French troops arrived in the Lebanese port of Naqoura, the first soldiers to bolster the UN force.
They are among 200 extra troops promised by France, as the UN struggles to build its force.
The UN wants 3,500 troops on the ground speedily, to be expanded later to 15,000. It says it is disappointed with the French contribution and wants other European nations to offer more help too.
Israel's fresh operation inside Lebanon came five days after a UN-brokered ceasefire ended the month-long conflict.
Lebanese Prime Minister Fouad Siniora said the Israeli raid was a naked violation of the ceasefire.
The Israeli army said the raid was to prevent arms being delivered to Hezbollah by Iran and Syria.
"Israeli army special forces operated deep inside Lebanon last night to foil terrorist operations against Israel," an army spokesman told AFP news agency.
He added that "all goals were achieved".
Reports on Hezbollah's TV station said Israeli commandos and two vehicles were flown into the area, some 100km (60 miles) north of the Israeli border, by helicopter.
The reports said they were driven back by Hezbollah fighters. Israeli missile strikes in the area were also reported.
The operation centred on the village of Bodai, west of the city of Baalbek.
The BBC's Jon Leyne at the scene says no-one there is quite sure what the target was, but speculation locally is that the Israelis may have been trying to capture a senior Hezbollah figure who lives in the village.
It is the first major incident between the two sides since the ceasefire came into effect.
The incident is not being seen in Israel as any sort of breakdown of the ceasefire, but a reinforcement of it, says the BBC's Rob Norris in Jerusalem.
The resolution said Israel should end all offensive military action and Hezbollah should end all attacks.
Israel has it will continue to carry out such actions until an expanded international military force is in place to prevent Hezbollah's re-armament.
Earlier Lebanese troops reached the southern border with Israel, where a vehicle carrying a Lebanese flag made a symbolic pass a few metres from the border at Kfar Kila.
The UN says 400,000 people have returned to homes in the south and in the heavily bombed southern suburbs of Beirut.
Pro-Syrian Lebanese President Emile Lahoud has praised what he called the victory of Hezbollah against Israel in a televised address to the nation.
He said he saluted Hezbollah leader Sheikh Hassan Nasrallah "who willed this victory to be a victory for all Lebanese and all the Arab peoples".
At his presidential retreat in Camp David, President George W Bush again condemned Hezbollah as a "force of instability".
"Sometimes it takes people awhile to come to the sober realisation of what forces create stability and what don't," he said.
In a separate development, an Israeli soldier was shot dead by a Palestinian gunman in the West Bank, the army said.
The incident happened near the city of Nablus, when militants opened fire from a car, one report said.