The Israeli army said three soldiers were killed in the initial raid, and four others were killed when their tank went over a land mine in southern Lebanon.
Israel also reported it killed another Hezbollah guerrilla as he tried to infiltrate a military base in northern Israel during a second raid.
Israeli Prime Minister Ehud Olmert called the first Hezbollah raid "an act of war" and held the Lebanese government responsible, vowing that the Israeli response "will be restrained, but very, very, very painful."
The Israeli military planned to call up thousands of reservists. Residents of Israeli towns on border with Lebanon were ordered to seek cover in underground bomb shelters.
Israel's forces are now fighting on two fronts, after the kidnap of an Israeli soldier by Palestinians in Gaza two weeks ago prompted an offensive in Gaza, reports CBS News correspondent Robert Berger.
CBS News chief foreign correspondent Lara Logan reports an air strike targeting Hamas commanders killed a Palestinian family of nine — including seven children.
"As bodies were pulled from the rubble here, you could feel the crowd, the anger of the crowd," Logan said in an exclusive report from the scene.
After initially claiming that its leaders had escaped harm, Hamas militants took over the intensive care unit of Gaza City's main hospital, where doctors said seven militants were in critical condition. The gunmen barred reporters from entering the unit and refused to say who was being treated.
Israel said it launched the air strike in the Sheik Radwan neighborhood, a Hamas stronghold, because Hamas commanders there were planning more attacks on Israel. Israel also said the home it attacked was a "meeting place for terrorists."
The Israeli army said its most wanted terrorist, Mohammed Deif was wounded, but Hamas denied it. Deif has narrowly escaped several assassination attempts in the past.
United Nations Secretary General Kofi Annan, on a visit to Rome, condemned the Israeli attack in southern Lebanon, reports CBS News correspondent Sabina Castelfranco. He also demanded the immediate release of kidnapped Israeli soldiers.
U.S. Assistant Secretary of State David Welch, on a visit to Cairo, said the capture of the two Israeli soldiers was "a very dangerous escalation" that "puts at risk all the effort that's being put forth by many to find a solution to the current situation."
Britain blamed Hezbollah for this latest escalation of mideast violence, condemning the kidnapping of the Israeli soldiers and the shelling of Israel, but said it wants a measured and proportionate Israeli response. France echoed that, reports CBS News correspondent Larry Miller, calling for the soldiers' unconditional release. Germany described the Hezbolah raid as an "irresponsible new escalation." There was support for Hezbollah from Syria, which claimed the "occupation provokes the Palestinians."
Wednesday's events threatened to complicate efforts to win Cpl. Gilad Shalit's release. The Shiite Lebanese Hezbollah said it had kidnapped the soldiers to help win the release of prisoners held in Israel. Hamas had made identical demands in seizing the Israeli soldier.
Jubilant residents of south Beirut, a stronghold of Hezbollah, and Palestinians in the Ein el-Hilwa refugee camp fired their guns in the air and set off firecrackers for more than an hour after the capture of the Israeli soldiers was announced.
By the afternoon, seven hours after the Hezbollah raid, Israeli military aircraft were striking large areas of southern Lebanon — targeting bridges, roads and Hezbollah positions in areas as deep as halfway between the Israeli border and the Lebanese capital, Beirut, Lebanese security officials said.
An Israeli army statement said the air force attacked more than 30 targets in south Lebanon to prevent the transfer of the kidnapped soldiers.
Several dozen ground troops entered southwestern Lebanon across the border where the soldiers were snatched, apparently only going a short distance in, witnesses said.
But Army Chief of Staff Lt. Gen. Dan Halutz warned the Lebanese government that the assault would widen. He said the military will target infrastructure and "turn back the clock in Lebanon by 20 years," if the soldiers were not returned, Israeli TV reported.
Hezbollah leadership has told CBS News that the capture of the two Israeli soldiers is yet further pressure to force Israel to release Palestinian detainees, reports Logan.
"We shall not surrender to arrogance and we will not negotiate with terrorists," Olmert said.
Hezbollah leader Sheik Hassan Nasrallah said he would not release the two captured Israeli soldiers except as part of a prisoner swap.
It would be an "illusion" if Israel thinks a military campaign can win the release of the soldiers, Nasrallah said.
"No military operation will return them," he told a news conference in Beirut. "The prisoners will not be returned except through one way: indirect negotiations and a trade."
Olmert said the attack was not an act of terror but an attack by a sovereign state on Israel. The Lebanese government, of which Hezbollah is a part, "must bear full responsibility," he said.
Hamas also appeared to toughen its demands for the safe return of Shalit, the 19-year-old soldier its militants seized two weeks ago, saying Hezbollah's actions strengthened Hamas' position.
"We have proven to this enemy (Israel) that the one option is the release of Palestinian, Lebanese and Arab captives. All captives, without exception," said Osama Hamdan, Hamas' spokesman in Lebanon.
"What happened has strengthened the issue of the captives, and the enemy will submit to our choice, which is the exchange of the captives in return for the release of the soldiers," he told Al-Jazeera television.
Hamas had previously demanded the release of some Palestinian prisoners in return for Cpl. Gilad Shalit's release.
Hamdan did not say whether Hamas had consulted with Hezbollah, but he said there may be subsequent "coordination and an understanding."
Hezbollah, which has been clashing with Israel for more than two decades, has repeatedly expressed its intent to kidnap Israeli soldiers to trade for Arab prisoners.
Israel occupied a small strip of southern Lebanon for 18 years before withdrawing in 2000 after high casualties on both sides raised public complaints in Israel. But Israel and Hezbollah still clash over a small sliver of border territory, Chebaa Farms, claimed by Lebanon.
Hezbollah fighters have controlled the Lebanese side of the border with Israel since Israeli forces pulled out. Lebanon is under U.N. and American pressure to disarm the Shiite guerrilla group and move its own military into the south, but the government has refused to do so, calling them a legitimate resistance group.
Israel has carried out several prisoner swaps with Hezbollah in the past to obtain freedom for captures Israelis. These include a January 2004 swap in which an Israeli civilian and the bodies of three Israeli soldiers were exchanged for 436 Arab prisoners and the bodies of 59 Lebanese fighters. In 1985, three Israeli soldiers captured in Lebanon in 1982 were traded for 1,150 Lebanese and Palestinian prisoners.