JERUSALEM — The Israeli military moved Tuesday to block tunnels it said Hezbollah has been building under the Lebanese border, saying it wanted “to nip them in the bud” before they posed a threat to Israeli civilians.

Israeli officials cast the operation as part of a broader strategy to curb Iranian influence in the region and, in particular, Tehran’s efforts to upgrade the weaponry of Hezbollah, Israel’s archenemy across the Lebanese frontier.

Prime Minister Benjamin Netanyahu of Israel said the early stages of the military effort, called Operation Northern Shield, had already been successful. “Whoever tries to harm the state of Israel will pay a heavy price,” he said in a statement.

The operation comes as Mr. Netanyahu faces growing legal troubles. On Sunday, the Israeli police recommended that he be indicted on bribery, fraud and other charges — the third in a series of corruption cases against him this year.