Israeli warships have entered Lebanese water to block ports, and its only international airport was closed after Israeli missiles blew up its runways.
Raids on targets across south Lebanon have killed at least 35 civilians.
The operation comes as Israel continues a separate offensive in the Gaza Strip where another soldier was captured.
The offensive in Lebanon follows a day of heavy fighting in which the Israelis suffered their worst losses on the border for several years.
Hezbollah guerrillas also fired volleys of rockets at the northern Israeli coastal town of Nahariya, killing one Israeli and injuring 14 others.
Israeli government spokesman Mark Regev told the BBC that Israel was responding to "an unprovoked act of aggression" by Lebanon.
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.
Syria should be "held to account", he said, adding that both Hezbollah and the Palestinian group Hamas are present in the country.
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.
Israeli leaders have also spoken of extending the blockade to include travel by land, although the BBC's Jim Muir in Beirut says this would be much harder to do, given the porous nature of the borders.
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. The station said three of its employees were hurt.
Israel said its jets hit 40 Hezbollah targets. Our correspondent says Beirut is largely cut off from southern Lebanon after Israeli missiles and bombs hit key roads and bridges.
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 if Lebanon did not deploy forces along its southern border, Israel would "not allow Hezbollah forces to remain on the borders of the state of Israel". Agriculture Minister Shalom Simchon said the Israeli government wanted to "change the rules of the game" in Lebanon and make its government "understand that it is responsible for what happens in Lebanon".
In Gaza, Israeli jets attacked the Palestinian foreign ministry building in Gaza City, injuring at least 10 people.
The operation follows the capture of Israeli soldier Cpl Gilad Shalit by Palestinians 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 is creating a volatile mixture.Last Mod: 20 Eylül 2018, 18:16