JERUSALEM - An Israeli air strike killed three Palestinians firing mortars at southern Israel yesterday, while Israel's leaders debated whether to pursue a truce with Gaza's Hamas rulers or launch a broad military offensive against extremists in the coastal strip.

In a related development, the father of an Israeli soldier held captive in Gaza by Hamas said his son pleaded for his life and appealed to the government not to abandon him in a newly received letter.

The Israeli attack came after extremists bombarded southern Israel with 20 mortar rounds in the space of an hour, and Hamas said the strike killed three members of one of its mortar squads.

At the time, Israel's top three officials - Prime Minister Ehud Olmert, Defense Minister Ehud Barak, and Foreign Minister Tzipi Livni - were discussing what to do about Gaza.

With four Israeli civilians killed by rocket and mortar attacks this year, Israel's leadership is under growing pressure to do something about the near-daily assaults. Barak and other officials have repeatedly said an Israel offensive is only a matter of time.

Gaza extremists have been bombarding southern Israel with rocket and mortar attacks for seven years, but increased their rate of fire after Israel pulled its troops and settlers out of the territory in 2005. The attacks ratcheted up after Hamas overran Gaza a year ago.

Israel's military has limited its reprisals to focused attacks, fearing a broad military campaign would result in heavy casualties on both sides.

One of Hamas' key bargaining chips is Gilad Schalit, the Israeli soldier it has been holding for nearly two years. Hamas hopes to trade the 21-year-old tank crewman for hundreds of Palestinian prisoners, but Israel has balked at releasing the prisoners, some of whom are serving time for fatal attacks on Israelis.

Hamas made good on a promise to former President Jimmy Carter and allowed the captured soldier to send a letter to his parents. It was delivered to them Monday.

Schalit's father, Noam, said yesterday that his son pleaded for his life and appealed to his government not to abandon him. He declined to quote directly from the letter.

The soldier has not been seen since he was seized in a cross-border raid in June 2006, when two other soldiers were killed. An audio recording of his voice and two other letters were released previously.

Egypt has been trying to broker a truce, but the cease-fire efforts have faltered over Israel's demand that Hamas free Schalit as part of the deal and a Hamas demand that Israel lift a blockade that has confined Gazans to their tiny seaside territory and deepened their poverty.

This week Hamas marks the first anniversary of its violent takeover of the coastal strip from security forces affiliated with moderate Palestinian Authority President Mahmoud Abbas. Hamas rejects the Jewish state's right to exist and has said publicly it wants a truce to rearm and regroup.

Adding urgency to Israel's debate about Gaza are assessments by its military intelligence that Hamas is rapidly upgrading its arsenal with Iranian assistance.

Brig. Gen. Yossi Baidatz, a senior intelligence officer, told the cabinet yesterday that Hamas now has rockets with a range of 12 miles, endangering a significant swath of southern Israel, according to the meeting participant.