Israel is imposing an air and sea blockade on Lebanon as part of a major offensive after two soldiers were seized by the militant group Hezbollah.
Israeli warships have blocked Lebanese ports, and its international airport was closed after Israeli bombing.
A Lebanese cabinet minister said the Israeli response was disproportionate, and called for a ceasefire.
Raids on targets across south Lebanon have killed at least 35. Two have died in Hezbollah attacks on Israel.
The operation comes as Israel continues a separate offensive in the Gaza Strip. An Israeli soldier was captured there last month.
The offensive in Lebanon 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. The captured men have now been named as Ehud Goldwasser, 31, and Eldad Regev, 26.
Hezbollah guerrillas also fired volleys of rockets at the northern Israeli coastal town of Nahariya, killing one Israeli and injuring 14 others.
They also fired seven rockets at the town of Safed, 15km (9 miles) inside the Israeli border, injuring 11 people. One woman later died of her wounds.
Hezbollah 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.
The Israeli army says several rockets have landed more than 20km (12 miles) south of the border, suggesting that Hezbollah has managed to extend their range.
Israeli government spokesman Mark Regev told the BBC that Israel was responding to "an unprovoked act of aggression" by Lebanon.
But Lebanese minister Naila Mouawad said Israel had responded disproportionately. The Lebanese government wanted a ceasefire, she said, calling for the two captured soldiers to be returned to Israel.
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.
France and Russia condemned Israel's "disproportionate use of force".
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.
An Israeli army spokesman said the airport was used to supply weapons to Hezbollah.
The blockade follows wide-ranging Israeli air raids on southern Lebanon, which killed at least 35 civilians.
Among the dead were two whole families - one of 10 people and one of seven - killed in the homes near the town of Nabatiyeh, officials said.
The Hezbollah television station al-Manar in southern Beirut was also hit, injuring three.
Israel said its jets hit 40 Hezbollah targets.
ISRAEL IN LEBANON
March 1978: Israel invades to stop Palestinian attacks
1982: Full-scale invasion reaching Beirut; pro-Israel forces massacre Palestinians
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: Prisoner swap between Hezbollah and Israel
Beirut is largely cut off from southern Lebanon after Israeli missiles and bombs hit key roads and bridges, correspondents say.
Israel has said it holds Lebanon responsible for the soldiers' capture and views it as an "act of war".
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.
Lebanese Prime Minister Fuad Siniora denied any knowledge of the Hezbollah operation and refused to take responsibility for the soldiers' capture.
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.
Israeli Defence Minister Amir Peretz said Israel would "not allow Hezbollah forces to remain on the borders of the state of Israel".
In Gaza, Israeli jets attacked the Palestinian foreign ministry building in Gaza City, injuring at least 10 people.
Israel has kept up air strikes and other military action against Gaza since the capture of Israeli soldier Cpl Gilad Shalit by Palestinian militants two weeks ago.
The BBC's World Affair's correspondent Nick Childs says the confrontations in Gaza and Lebanon are ringing alarm bells among world leaders.
He says the combination of an untried and apparently uncertain Israeli government, plus tensions that could easily extend to Syria and Iran, are creating a volatile mixture.
ISRAEL BLOCKADES LEBANON
Israel targets Lebanon by land, air and sea: enforcing naval blockade, bombing Beirut airport and shelling Lebanese towns
Bombs hit al-Manar TV HQ in Beirut and Baalbek antenna
Hezbollah targets Kiryat Shmona, Nahariya and Safed in Israel