Israel says it is planning to retaliate against Lebanon
Planes struck outposts of the Hezbollah militant group in south Lebanon, as well as roads, killing two civilians.
Israel has called up reserve troops, signalling a large-scale campaign, as operations continue to free a soldier seized by Palestinians in Gaza in June.
Israel's PM Ehud Olmert said the attack was an "act of war" by Lebanon.
Mr Olmert has said he holds Lebanon responsible for the fate of the two soldiers and that it would pay a "heavy price".
The prime minister has called an emergency cabinet meeting to discuss further action, although he has already ruled out negotiations.
"The Lebanese government, of which Hezbollah is a part, is trying to shake regional stability," he said at a press conference in Jerusalem.
"We are already responding with great strength," he said, threatening "very painful and far-reaching" action.
Soldiers' search
Israeli ground troops have entered southern Lebanon to search for the two soldiers, for the first time since Israel ended its occupation of south Lebanon six years ago.
HAVE YOUR SAY Hezbollah and the Lebanese Government have brought this assault upon themselves
Daniel Schay, Edenvale, South Africa
Send us your comments In pictures: Border clashes
The news of the clashes comes as a major Israeli offensive is under way in the Gaza Strip. An Israeli soldier was kidnapped by Palestinian militants in Israel over two weeks ago.
Overnight, Israel carried out an air strike on a Gaza City house, killing at least six people and injuring 15.
On Wednesday morning, Hezbollah launched dozens of Katyusha rockets and mortar bombs at the Israeli town of Shlomi and at Israeli outposts in the Shebaa Farms area.
Later on Wednesday, Hezbollah said its fighters had destroyed an Israeli tank attempting to cross the border. An Israeli military spokeswoman said there had been a number of casualties.
Two civilians were killed when Israeli planes bombed a road bridge on major route though southern Lebanon.
Civilians in northern Israel have been told to stay in their shelters.
The UN representative in Lebanon, Geir Pedrson, has condemned the escalation and called on Hezbollah to release the soldiers.
Call for swap
Hezbollah said it captured the two Israeli soldiers at 0904 (0704 GMT).
A statement from the group said the two were taken to a "safe place". It did not mention whether they were alive or dead or injured.
"Fulfilling its pledge to liberate the prisoners and detainees, the Islamic Resistance... captured two Israeli soldiers at the border with occupied Palestine," the Hezbollah statement said.
Hezbollah captured three Israeli soldiers in 2000. They died during the operation, but four years later, the group was able to exchange their bodies for 430 Palestinians and Lebanese held in Israeli jails.
BBC Middle East analyst Roger Hardy says the capture of two Israeli soldiers is a dramatic gesture of solidarity with the Palestinians - and at the same time adds to the pressures on the Israeli government.
Complicating the picture is the fact that the Lebanese group has the backing of both Syria and Iran.
Israel and American officials are already saying Syria must bear some of the blame for the capture of a young Israeli soldier in Gaza last month - because it plays host to part of the Hamas leadership.
Pressure on Syria - as well as on the Lebanese government - will now intensify, our analyst adds.
Israel has launched an incursion into southern Lebanon in what they claim is a search for two Israeli soldiers. The soldiers were taken Wednesday following an attack by Hezbollah, a Lebanese militia, that had made an incursion into Israel. 

Three Israeli soldiers died and eleven were wounded when army transports patrolling at the Israeli-Lebanese border were attacked on Wednesday morning, near the Israeli village of Zar'it. Hezbollah also fired mortars and long-range rockets at the Israeli town of Shlomi and nearby communities. Six Israeli civilians were injured by the artillery fire.

After the attack two soldiers were found to be missing. Israeli troops and tanks then entered southern Lebanon, having claimed the soldiers were kidnapped. Following the incursion, five more soldiers were killed, four of them when an Israeli tank hit a mine. Hezbollah said one of its members died.

The Israeli air-force targeted several roads, bridges and Hezbollah outposts in an attempt to stop militants from moving the soldiers, Israel said. Two civilians were killed in an air raid on one of the bridges, while 23 others have been injured. Israeli artillery and gunboats also attacked other targets on Lebanese soil.

Later, Hezbollah said they had destroyed an Israeli tank which had crossed the border into Lebanon.

Ehud Olmert, Israel's Prime Minister, blamed the attack on the Lebanese government calling it "an act of war" and vowed to deliver a "very painful and far-reaching" response. Israel Defense Forces Chief of Staff Dan Halutz told Israel's Channel 10 that if the soldiers are not returned "we will turn Lebanon's clock back 20 years".

Hezbollah Secretary-General, Sheik Hassan Nasrallah, hailed what he called the capture of the two soldiers calling them "our natural, only and logical right". He also said that the soldiers were taken to "a far away place" and that the only way to get them back was through an exchange with Lebanese and other Arab prisoners in Israeli jails.

The Israeli cabinet is in an emergency meeting and has yet to make an official statement about the situation. PM Ehud Olmert said previously that swapping of prisoners is not an option.

Hezbollah's announcement of their captures led to celebration scenes in a Hezbollah-strong suburb in Beirut with firing of guns in the air and handing out candy to children.

The Lebanese government issued a statement after an emergency meeting of the cabinet saying that it was not informed of the intentions of Hezbollah and that it does not endorse the group's actions. Prime Minister Fouad Siniora was quoted as saying that "the government was not aware of and does not take responsibility for, nor endorses what happened on the international border". 

Hezbollah currently has two sitting members on the Lebanese government's ruling coalition.

The view recognized by the United States is one that condemned the attacks, but acknowledged that Lebanon had little say over Hezbollah in the south. The White House  said the militant group's violent actions were supported by Iran and Syria.

Israel has filed a complaint with the United Nations which called for the Security Council to enforce resolutions urging Lebanon to extend its authority throughout its territory and to disarm its militias.