Lebanese ministers have called for a ceasefire with Israel, saying that all means should be used to end "open aggression" against their country.
Israel says it is responding to unprovoked aggression
International calls for restraint are growing, with Russia, France and the EU saying Israel's response to the capture of two soldiers was disproportionate.
Meanwhile Israeli jets bombed the main Lebanese army air base in Bekaa Valley.
Israel is imposing an air and sea blockade on Lebanon following the two soldiers' capture by Hezbollah.
Israeli warships have blocked Lebanese ports, and its international airport was closed after Israeli bombing.
Raids on targets across south Lebanon have killed at least 48 people, mostly civilians, while an Israeli civilian died in Hezbollah attacks on Israel.
People on both sides of the border have been fleeing.
Thousands of tourists - many of them Gulf Arabs - have been crossing into Syria, and Cyprus is planning a special flight from Damascus to rescue stranded Cypriot and other European nationals.
Israeli government spokesman Mark Regev said Israel was responding to "an unprovoked act of aggression" by Lebanon.
The operation comes as Israel continues a separate offensive in the Gaza Strip. An Israeli soldier was captured there last month.
The two Israeli soldiers captured by Hezbollah have been named as Ehud Goldwasser, 31, and Eldad Regev, 26.
Israel expressed concern that they would be taken to Iran, but Tehran's foreign ministry described the idea as "absurd".
Lebanese Social Affairs Minister Naila Mouawad said the two men should be returned to Israel.
She told the BBC the government was not aware of the Hezbollah operation and did not support it, but this did not excuse Israel's actions.
"We think that the Israeli response is too hard ... on the people of Lebanon, who have been taken hostage," she said.
ISRAEL IN LEBANON
March 1978: Israel invades to stop Palestinian attacks
1982: Full-scale invasion; Israel occupies Beirut; pro-Israel militias massacre Palestinian refugees
May 1983: Israel pulls back, but keeps "security zone"
February 1992: Israeli air strike kills Hezbollah leader
1996: Israel launches "Grapes of Wrath" raids on Hezbollah; 100 civilians die under Israeli shelling of UN base at Qana
May 2000: Israel withdraws troops from Lebanon
January 2004: Prisoners-bodies swap agreed between Hezbollah and Israel
She said Lebanon was in a catastrophe, but the government was unable to disarm Hezbollah by force.
Hezbollah has said the captured soldiers will not be returned without a release deal for Palestinian, Lebanese and other Arab prisoners held in Israeli jails.
The EU said it was preparing to send foreign policy chief Javier Solana to the region, while the Arab League said it would discuss the crisis on Saturday.
US President George Bush described Hezbollah as a "group of terrorists who want to stop the advance of peace".
Speaking in Germany, he said Israel had the right to defend itself, but its action should not weaken the Lebanese government.
UK Foreign Secretary Margaret Beckett said that while Israel needed to ensure its own security it should do so in a measured way which avoided civilian death and suffering.
The offensive follows a day of heavy fighting in which the Israelis suffered their worst losses on the border for several years.
Eight soldiers were killed and two were injured, in addition to the two captured in a Hezbollah ambush.
Hezbollah guerrillas also fired volleys of rockets at several towns in northern Israel.
It has threatened to attack the Israeli port city of Haifa if Israel bombs Beirut. Israel has warned people in the Lebanese capital's southern suburbs to evacuate.
But it is not clear whether Haifa, which is 30km (19 miles) from the Israeli border, is within range of Hezbollah's rockets, several of which have landed more than 20km (12 miles) inside Israel.
An Israeli military spokesman said Israeli naval ships had entered Lebanese waters to block the transfer of "terrorists and weapons to the terror organisations operating in Lebanon".
Earlier, three missiles hit runways at Beirut airport, the country's only international airport, forcing its closure. Flights have been diverted to Cyprus.
Hezbollah's political wing is a significant force in Lebanese politics and has one government minister, while its powerful military wing has controlled the border zone since Israeli forces pulled out in 2000.
ISRAEL BLOCKADES LEBANON
Israel targets Lebanon by land, air and sea: enforcing naval blockade, bombing Beirut airport and shelling Lebanese towns
Jets bomb Lebanese army air base at Rayak and Baalbek TV transmitter in Bekaa Valley
Shelling from both sides is heaviest over Lebanon's southern border
Hezbollah targets Kiryat Shmona, Nahariya and Safed in Israel