The Islamic Resistance, the military arm of Hezbollah, announced the capture in a statement broadcast by its television station.
The Shiite militant group saying it captured the Israelis to secure the release of detainees held in Israeli prisons.
“At 09h05 this morning, the Hezbollah captured two Israeli soldiers near the border with occupied Palestine, and the captives have been moved to a safe area,” Hezbollah said in a statement faxed to news agencies.
Israeli military confirmed the kidnapping, saying it has “serious concern” about fate of the two soldiers. The military said the capture probably took place near the collective farm of Zarit, on the border with Lebanon on what it said was Israeli territory.
Jubilant residents of south Beirut, a stronghold of Hizbollah, fired their guns in the air and set off firecrackers for more than an hour after the reports of the capture of the Israeli soldiers
In the main Palestinian refugee camp of Ein el-Hilweh in Sidon, in southern Lebanon, Palestinians set fireworks.
Israeli aircraft are have now begun attacking roads, bridges and Hezbollah guerrilla positions in southern Lebanon, in an apparent attempt to block any attempt to move the captured soldiers away from the border in an attempt to prevent an Israeli rescue mission.
Israeli tanks are also shelling southern Lebanon.
An Israeli security source says at least two Israelis have been killed in cross-border attacks by Hezbollah guerrillas from Lebanon. Details on the deaths aren’t immediately clear, the Israeli army hasn’t commented but has confirmed some casualties.
Two Lebanese civilians have also been killed and five others wounded.
The Israeli military, meanwhile, ordered its residents near the border to seek cover in underground bomb shelters.
Israeli jets flew over Sidon and nearby areas and Lebanese army anti-aircraft opened up at them, the Lebanese officials said. Three bridges were damaged, the officials said.
The planes also attacked positions near the village of Sultanieh further east on the border, and al-Manar TV said power was cut off in the village.
Earlier, the Syrian-backed Hezbollah had fired dozens of Katyusha rockets and mortar bombs at Israeli border posts and a town, wounding four Israeli civilians.
Israeli gunners retaliated, firing artillery shells into the outskirts of four Lebanese border villages while Israeli soldiers exchanged gunfire with guerrillas in the area.
The fighting allegedly began when at least two rockets fired from Lebanon exploded near Shlomi, an Israeli frontier town about 15km east of the Mediterranean coast. Hezbollah also attacked Israeli posts in the Israeli-occupied Shebaa Farms area to the east, Lebanese security sources said.
An Israeli cabinent meeting has been called for later in the day to discuss the crisis, but Israeli Prime Minister Ehud Olmert says Hezbollah will pay a “heavy price” for their actions, “These are difficult days for the state of Israel and its citizens.”
“There are people … who are trying to test our resolve,” he said during a reception for visiting Japanese Prime Minister Junichiro Koizumi.
“They will fail and they will pay a heavy price for their actions,” he added.
This is the third Israeli soldiers to have been kidnapped this month; earlier Palestinian militants abducted a 19 year old soldier from a border post, triggering a major and ongoing Israeli military incursion in the Gaza Strip.
The latest clashes between the Palestinians and the Israelis came when Israel dropped a quarter-ton bomb on a residential building in Gaza, killing at least six people, including two children and injuring about 30 people.
Israel says the building was owned by Hamas leaders who were in it at the time of the strike. Hamas says its members escaped the attack but vowed a “strong and painful” response, a statement from Hamas’s military wing the Ezzedine al Qassam Brigades said it would now target Israeli civilians.
“Our reaction to this massacre will be painful and strong for the Zionists and we will make the enemy leadership sorry for their crime,” the Brigades said in a statement.
“This new crime is a changing point in the rules of the battle. We will choose the rules of the game in the coming period. Our message to the Zionists is that your leaders are leading you to violence from which no one will be safe and when they target civilians they decided for you to be the target of our resistance,” the statement added.
The air strike was preceded by a large- scale incursion into the central Gaza Strip, east of the Deir al-Balah refugee camp.
Israeli Prime Minister Ehud Olmert has flatly refused to negotiate with Hamas or free Palestinian prisoners in exchange for kidnapped soldier, 19-year-old Corporal Gilad Shalit.
Despite international criticism that Israeli force has been disproportionate, Mr Olmert has defended the scale of the operation, vowing the assault would continue “in places, in time, in measures” at Israel’s convenience.
Meanwhile, a column of tanks escorted by bulldozers entered 700 metres into the south of the Gaza Strip taking up positions around the village of El Karara.
With Israel’s punishing aerial campaign now in a third week, at least 60 Palestinians have been killed in the operation, on top of one Israeli soldier killed by friendly fire.
Defence sources said that the government had given the military authority to continue, and if necessary, intensify the offensive, with infantry and armour poised to carry out “in-depth” incursions.
Palestinians in northern Gaza on Tuesday fired a homemade rocket against Israel, causing no casualties or damage.
In a statement issued after his weekly cabinet meeting, Palestinian Prime Minister Ismail Haniya warned against a “humanitarian tragedy” developing in Gaza as a result of Israel’s continuing “blockade”.
Aid groups have also expressed concern about the difficulties of providing assistance to one point four million people living in Gaza.