Mr Sharon also accused Syria and Iran of backing the attacks in a disputed border zone.
Israel responded with air strikes and artillery fire.
Correspondents say the escalating tension on the Israel-Lebanon border has raised fears of a new military front opening in the Middle East.
Stability threatened
"We saw that Syria is giving support and backing to what is going on," Mr Sharon said during a visit to the army's Northern Command headquarters, a day after a soldier was seriously wounded in a Hezbollah attack.
"We are ready and prepared for all actions that we will take as required. We have no intention that the situation here will return to what it was," Mr Sharon said.
He also added that the attacks had "Iranian approval, Iranian assistance".
Israeli Foreign Minister Shimon Peres said on Wednesday that attacks by Hezbollah could have "alarming consequences on the stability of the region".
He said Israel had received "alarming information"
that Hezbollah was planning to increase its attacks.
Israel's security cabinet met on Thursday to discuss the tensions on the border with Lebanon, as well as the other violence in the Middle East.
Troops withdrawn
Interior Minister Eli Yishai told Israel radio that the
security cabinet had decided on a "most severe" response to the Hezbollah attacks, but gave no details.
Syrian troops pulled back to new positions in eastern Lebanon on Thursday in what experts say is an attempt to lessen direct confrontation with Israel.
Twice last year Israel hit Syrian troops in Lebanon with air strikes in retaliation for Hezbollah attacks.
Several dozen truckloads of Syrian soldiers who left posts in central Lebanon on Wednesday set up in eastern Lebanon's Bekaa valley, and at least 20 trucks of soldiers crossed into Syria, witnesses said.
The Lebanese army said it and Syria had decided to move the troops toward the Lebanese-Syrian border in line with the treaty that ended Lebanon's 1975-1990 civil war.
Related to this story:
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Israel and Hezbollah exchange fire
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Analysis: Hezbollah plays for high stakes
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Gunmen fire on Israel from Lebanon
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