Militants in Hamas-ruled Gaza bombarded southern Israel with rockets Thursday and Israel pounded back with air and ground fire, the latest spate of violence that has pushed peace efforts to the sidelines.

Israeli leaders made clear they had no intention of pulling back until the rocket assaults on Israeli border communities halt.

Twenty-three Palestinians were killed in fierce clashes in the seaside territory on Tuesday and Wednesday, including the son of Gaza's Hamas strongman, Mahmoud Zahar, and a 12-year-old boy who died along with his father and uncle in a bungled Israeli airstrike. A foreign volunteer on an Israeli border farm was killed by a Hamas sniper.

Palestinian President Mahmoud Abbas, Hamas' bitter rival and Israel's moderate partner in newly resumed peace talks, denounced what he called the Israeli "massacre" in Gaza.

Hamas, the Islamic militant group that rejects Israel's right to exist, has intensified its direct involvement in the assaults on Israel as a result of the escalating violence. The group, which had let other militant factions take the lead in attacking Israel since it wrested control of Gaza in June, claimed it fired 24 rockets early Thursday, after launching 79 rockets and mortars on Wednesday.

Other groups said they fired an additional four rockets and eight mortar rounds.

Israeli police said 18 rockets and mortars landed in Israel by midday. One rocket slammed into the side of a house, slightly injuring two people, police said.

Israelis fired at northern Gaza from the air and ground, targeting rocket squads and areas militants frequently use to fire projectiles. No injuries were reported, Hamas security said.

"We have stepped up and will further step up the pressure and the attacks on the terror activists in the Gaza Strip, and if necessary, we will step up the attacks even further," Defense Minister Ehud Barak said Wednesday night. "It isn't simple, but our goal is to stop the Qassam rocket fire."

Militants have launched some 4,000 of the crude rockets and mortar rounds at southern Israel since Israel evacuated Gaza in the summer of 2005 after a 38-year occupation. The rockets have killed 12 people since 2001 and sown panic in border areas, where people are frequently forced to rush to take cover when sirens alert them to incoming projectiles.

Militants have been extending their reach as well, with one Iranian-made rocket recently traveling some 10 miles inside Israel's borders.

Israeli Vice Premier Haim Ramon expressed confidence on Thursday that the military strikes, combined with stiff economic sanctions that Israel and the international community have imposed on Gaza, would have the desired effect.

"We already see Hamas wanted a cease-fire," he said. In recent weeks, Hamas had sent out feelers to Israel about a cease-fire, but Israel rejected them.

The deepening violence has clouded the resumption of Israeli-Palestinian peace talks. Abbas took the unusual step Wednesday of calling his foe Zahar to express condolences for his son's death. Shortly after his militant son was killed on Tuesday, Zahar accused Abbas of complicity by negotiating with Israel.

Hamas' supreme leader, speaking from his base of exile in Damascus, said Wednesday that Israeli raids on Gaza made the group less likely to negotiate any truce with Israel.

Khaled Mashaal also said the military action would hurt chances of Hamas' releasing an Israeli soldier it has held captive since 2006, Cpl. Gilad Shalit.

"What you are doing will deny you of any plan you could be betting on: No exchange for Gilad Shalit and no truce," Mashaal said at a news conference.

At the funeral of two militants killed Wednesday in an Israeli airstrike, mourners demanded revenge and vowed the armed struggle against Israel would continue.

"We mourn our comrades today, but vow to God that the march of resistance will not stop," said Abu Attaya, spokesman for the militants' small faction, the Hamas-allied Popular Resistance Committees.

Visiting the rocket-battered Israeli town of Sderot on Wednesday, U.N. envoy Robert Serry called the rocket attacks "random terror," while also criticizing Israel's Gaza raids. He called for a cease-fire.