Hezbollah, the Lebanese militia, fired missiles into northern Israel on Tuesday that injured at least two people, emergency officials said, amid a fresh diplomatic push to end months of clashes along the border.

Hezbollah said that it had launched two separate attacks into Israel — one aimed at Israeli soldiers and the other at a police building in the northern town of Kiryat Shmona.

A 15-year-old boy and a 47-year-old woman were seriously wounded in Kiryat Shmona, according to Magen David Adom, Israel’s nonprofit emergency medical service. They had gotten out of the car they were traveling in when an anti-tank missile hit nearby, only to be injured when another landed, said Ofir Yehezkeli, Kiryat Shmona’s deputy mayor.

Israel and Hezbollah — an ally of Hamas in Gaza — have engaged in near-daily cross-border strikes since the deadly Hamas-led Oct. 7. attacks in Israel. The clashes have displaced more than 150,000 people from their homes on both sides of the Israel-Lebanon border.

The United States and others have engaged in diplomatic efforts to reduce the tensions. A Western diplomat said on Tuesday that France had presented a proposal to Israel, Lebanon’s government and Hezbollah. The French proposal was first reported by Reuters.

The proposal details a 10-day process of de-escalation and calls for Hezbollah to withdraw its fighters to a distance of 10 kilometers (six miles) from Lebanon’s border with Israel, according to the diplomat, who is involved in the talks and who requested anonymity to discuss the sensitive deliberations. The diplomat said that France’s foreign minister, Stéphane Séjourné, presented the proposal in writing to Lebanon’s government last week while on a visit to the country.

Lebanon’s Foreign Ministry confirmed that the government had received the proposal. The French Foreign Ministry and Hezbollah did not immediately respond to requests for comment.

In recent weeks, Israel has warned that unless a diplomatic solution is reached, it would have to use military force to stop Hezbollah’s attacks in order to allow for tens of thousands of Israelis to return to their homes.

Patrick Kingsley, Roger Cohen and Cassandra Vinograd contributed reporting.