Lieutenant-General Dan Halutz, the Israeli army chief of staff, warned the Lebanese government that Israel would attack its infrastructure and "turn back the clock in Lebanon by 20 years" if the soldiers were not returned, Israeli TV reported.
Ehud Olmert, the Israeli prime minister, described the Hezbollah raid as an "act of war" by Lebanon and promised a "very painful and far-reaching response".
The Israeli military carried out air attacks, and used tanks and gunboats in retaliatory strikes.
Two Lebanese civilians were killed in an Israeli air strike on a coastal bridge in Qasmiyeh.
Four other bridges in the south were hit and five Lebanese were wounded, Lebanese security sources said.
Sayyed Hassan Nasrallah, the leader of Hezbollah, said Israeli attacks would not lead to the release of the captured soldiers.
Hezbollah said it had captured the pair to secure the release of detainees held in Israeli prisons.
"Any military operation will not lead to returning the [Israeli] captives. The only means is indirect negotiation and thus a swap," Nasrallah said.
"If the enemy is thinking of escalation and that it wants Lebanon to pay a price then ... we are ready and willing, more than the enemy expects."
"We are already responding with great strength"
Hezbollah said earlier that the soldiers had been transferred to a "safe place".
The group's supporters set off fire crackers and distributed sweets in the streets of Beirut after it issued its claim. Similar scenes were reported across Lebanon.
Seven Israeli soldiers were killed during the Hezbollah raid and clashes that followed.
Hezbollah and the Lebanese authorities said Israeli forces had not crossed far into Lebanese territory.
Israeli troops have not struck far into Lebanon since they withdrew from the southern border area in 2000 after Hezbollah's Shia fighters waged an 18-year campaign against them.
Olmert called a special cabinet session for 1700 GMT to discuss further military action.
"It is an act of war by the state of Lebanon against the state of Israel in its sovereign territory," he said.
"We are already responding with great strength ... The cabinet will convene tonight to decide on a further military response by the Israel Defence Forces [Israeli military]."
The Israeli army shelled towns in
The Palestinian Hamas government praised Hezbollah's capture of the soldiers.
"This operation, which comes two weeks after the capture of an Israeli soldier in Gaza, shows the weakness of the Israeli army which boasts that it is an invincible army," the group said in a statement.