Israel threatened "very painful and far-reaching" action
Hassan Nasrallah said if Israel wanted to escalate the crisis his forces were ready for confrontation.
Israel launched an assault in southern Lebanon using planes, tanks and gunboats following the capture.
Three Israeli troops were killed in Hezbollah's cross-border raid and four more died in the subsequent offensive.
The second incident occurred when a tank involved in the ground operation hit a mine.
If the Israeli enemy wants escalation, we are ready for the confrontation
Hassan Nasrallah
Hezbollah leader News conference
Roads and Hezbollah outposts were hit and two civilians killed as Israeli forces entered Lebanon, in their first incursion since 2000.
Israeli Prime Minister Ehud Olmert described Lebanon's actions as an "act of war".
He said he held Beirut responsible for the fate of the two soldiers and that it would pay a "heavy price".
Emergency meeting
However, Lebanese Prime Minister Fuad Siniora said he had not known about the Hezbollah operation and refused to take responsibility for the soldiers' capture.
"The government was not aware of and does not take responsibility for, nor endorses what happened on the international border," Reuters news agency quoted him as saying.
Mr Olmert was due to hold an emergency cabinet meeting to discuss further action, although he has already ruled out negotiations.
Israel has filed a complaint with the United Nations, urging the Security Council to enforce resolutions calling on the Lebanese government to disarm militias and extend its authority throughout its territory.
In Washington, the White House has called for the immediate release of the captured Israeli soldiers, saying it held Iran and Syria responsible for the attack.
The news of the clashes comes amid a major Israeli offensive in the Gaza Strip. Israel has been trying to secure the release of a 19-year-old soldier, Cpl Gilad Shalit, who was kidnapped by Palestinian militants on 25 June.
'Dreaming'
Hezbollah is seeking the return of Palestinian, Lebanese and other Arab prisoners held in Israeli jails.
Mr Nasrallah said any invasion of Lebanese territory would be met by force.
"The prisoners in our hands will not return to Israel except through indirect negotiations and exchange of prisoners and peace," he said.
"If the Israelis are thinking about carrying out a military operation to recover them they are dreaming."
"We are not seeking escalation, we don't want to lead the region into war. However, if the Israeli enemy wants escalation, we are ready for the confrontation."
He said what Hezbollah had done was the "only feasible path" to freeing detainees in Israeli jails, and "our natural right".
The operation had been planned for several months, he added, long before the capture of Cpl Shalit in Gaza.
Major campaign
UN Secretary General Kofi Annan both condemned Israel's Lebanon offensive and called for the soldiers' release.
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
Army Chief of Staff Lt-Gen Dan Halutz said the Israeli military would "turn back the clock in Lebanon by 20 years" if the soldiers were not returned.
Several thousand reservists will be deployed along the border, officials say.
In other developments:
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.