JERUSALEM — Israel’s leaders ratcheted up their rhetoric on Sunday after an Israeli airstrike killed four Palestinian militants in Hamas-run Gaza, but both sides left the door open to restoring a truce that has all but broken down.

The prime minister of Israel, Ehud Olmert, lay responsibility for a rise in violence recently “entirely with Hamas and the other terrorist organizations active in the Gaza Strip.” He said he had asked defense and legal officials to complete their work on formulating options for Israeli action in Gaza.

Mr. Olmert was speaking at the start of the weekly cabinet meeting shortly after the four militants were killed in northern Gaza. The men, members of the small Popular Resistance Committees, were on their way to fire rockets or mortars against Israel, according to the group and the Israeli military.

At least 15 Gaza militants, many of them from Hamas, have been killed in almost two weeks of clashes with Israel. Israeli officials say that about 20 mortar shells and rockets were fired from Gaza over the weekend, including at least two imported, longer-range Katyusha-type rockets fired by Hamas at the Israeli coastal city of Ashkelon.

A woman, 80, was lightly wounded by shrapnel in the Israeli border town of Sderot, and several Israelis were treated for shock, medics said. Israel has kept the border crossings into Gaza almost completely sealed since hostilities broke out again in early November, halting regular supplies of basic goods and fuel.

Israel’s transport minister, Shaul Mofaz, a former defense minister and army chief of staff, told the Israeli news website Ynet that Israel should “stop talking and launch a personal targeted killing policy” against the leaders of Hamas, the militant Islamic group that took over Gaza in 2007.

Zeev Boim, the housing minister, also called for “an action or series of actions to remove Hamas from power in Gaza,” adding that closing the crossings only harms the Palestinian population, “most of whom are not involved in terror.”

But Mr. Olmert said that his government had always acted in such situations with “equanimity and sagacity” and would continue to do so now.

The defense minister, Ehud Barak, who is said not to favor a large-scale military operation in Gaza, said that no one should regret any month that passes quietly. “Hotheadedness is not a replacement for policy,” he said.

In Gaza, Hamas leaders continued to express their interest in a renewal of the Egyptian-brokered truce that took effect in June. Mahmoud Zahar, a senior Hamas official, said that Arab parties were also “emphasizing the commitment of Israel” to the truce, suggesting that Hamas had received messages to that effect.

To a large extent, the truce is dependent on Hamas being able and willing to rein in smaller groups like the Popular Resistance Committees. Mr. Zahar said on Sunday that “other factions” would convince them to stay in line.

The calm started to unravel almost two weeks ago when an Israeli force entered Gaza for the first time in five months to destroy a tunnel Israel feared Hamas might use to abduct soldiers in a cross-border raid.

“Hamas saw that as an attempt by Israel to redesign the rules of the game,” Ehud Yaari, a prominent analyst on Arab affairs, said in a telephone interview, referring to Israel’s decision to act based on intelligence information.

The Hamas reaction, culminating in the firing of Katyusha-type rockets at Ashkelon, was meant to signal the group’s rejection of any change in the rules, Mr. Yaari said. “They were firing in order to re-establish the cease-fire,” he said.