The Lebanese group said on Wednesday that it had captured the pair to secure the release of detainees held in Israeli prisons.
"In order to fulfil a promise to free the prisoners and detainees, the Islamic Resistance captured at 9:05am [0605 GMT] two Israeli soldiers at the borders with occupied Palestine," Hezbollah said referring to its military wing.
"The two prisoners were moved to a safe place," it said.
The Syria-backed group "expressed readiness to start a process of negotiations for a prisoner exchange deal with Israel", a Lebanese political source said.
Hezbollah refused to comment but its leader, Sheikh Hassan Nasrallah, will announce the group's position at a news conference in coming days.
Hezbollah, the only Lebanese faction to retain its weapons after the 1975-90 civil war, is also a political party with 14 members of parliament and two cabinet ministers.
'Act of war'
The Israeli defence ministry confirmed the kidnapping and said it held the Lebanese government "directly responsible" for their fate and safe return.
Ehud Olmert, the Israeli prime minister, convened an emergency meeting of cabinet ministers for 7pm (1600 GMT) and said that those who tried to test Israel's resolve would "pay a heavy price".
He described the kidnapping as an "act of war" as he promised a "very painful and far-reaching" response.
Lebanese security sources said Israeli aircraft retaliated to the kidnapping and earlier cross-border attacks by Hezbollah by bombing three bridges in south Lebanon.
Two Lebanese civilians were killed and five people wounded in the strikes, Lebanese security sources said.
Separately, the Israeli medical rescue service Zaka said three Israelis were killed and eight wounded in the Hezbollah attacks.
The identities of the casualties were not immediately known.
Hezbollah said it had destroyed an Israeli tank that had entered Lebanon after its cross-border raid, inflicting casualties on its crew.
Aljazeera television said seven Israelis had been killed in Wednesday's border violence.
Lebanese security officials put the toll at six, saying three Israeli soldiers were killed in the morning raid during which the two soldiers were captured, and that three other soldiers died when their tank exploded on the border.
Meanwhile, Israel's army radio reported that ground forces had entered Lebanon to search for the missing soldiers.
Israel's Channel 10 television said a reserve infantry division had been mobilised and was expected to be sent to Israel's northern border with Lebanon.
Israeli troops have not struck deep into Lebanon since they withdrew from a southern border strip in 2000 after waging an 18-year war with Hezbollah's Shia fighters.
The US assistant secretary of state, David Welch, on a visit to Egypt, told reporters that the capture of the soldiers, if confirmed, was "a very dangerous escalation".
"We call for the release of those who have been captured if, as we understand, the news is true," he said.
Britain's foreign office minister, Kim Howells, said: "We call on all parties to take actions to promote a rapid and peaceful resolution of the crisis and urge that any Israeli action be both measured and proportionate."
The UN envoy to Lebanon, Geir Pedersen, called on Hezbollah to release the soldiers and urged all parties to "exercise maximum restraint and avoid any further escalation".
The Hezbollah attack coincided with a two-week-old Israeli raid in the Gaza Strip, ordered partly in retaliation for the abduction of a soldier by Palestinian fighters last month from a border post.
Osama Hamdan, the spokesman of Hamas in Lebanon, said Wednesday's kidnapping strengthened the position of his Palestinian movement.
"We have proven to this enemy [Israel] that the one option is the release of Palestinian, Lebanese and Arab captives. All captives, without exception," Hamdan told Aljazeera television.
Hamdan said they may be "co-ordination and an understanding" between Hamas and Hezbollah, suggesting they might act together over their demands.