Palestinian militants fired rockets far into southern Israel late Tuesday and early Wednesday and Israel responded with airstrikes in Gaza. Tensions were running high after a stray Israeli mortar shell killed three Palestinian youths and a 60-year-old man as Israel responded to a rocket attack a day earlier.

In a separate attack on Tuesday night, the Israeli Air Force killed four militants in a car, all members of Islamic Jihad, the organization and the Israeli military said. The army said the men were preparing to launch rockets at Israel.

At least one Katyusha-type rocket hit a street in the center of the southern Israeli city of Beersheva on Wednesday morning, slightly wounding one man and causing damage to nearby houses. Several mortar shells also fell on the Israeli side of the border with Gaza, the Israeli military said.

On Tuesday night, a longer-range rocket fell just short of the Israeli port city of Ashdod. The Israeli Air Force strick back at the spot from which the rocket was fired and killed a militant there, according to the Israeli military.

Gaza militants have fired a trickle of short-range rockets and mortar shells at southern Israel in recent months, but the longer-range weapons that reached deeper into Israel on Tuesday and Wednesday have been much rarer since the end of Israel’s military offensive in Gaza in Januray 2009.

Islamic Jihad claimed responsibility for the latest rocket fire.

The violence came amid a sharp increase in tensions along the Israel-Gaza border in recent days. Hamas, the Islamic militant group that controls Gaza, has fired more than 60 mortar shells and rockets at Israel since Saturday, and Israeli warplanes and artillery units have carried out repeated attacks. Both sides claim they are retaliating and not seeking an escalation in the conflict, but fears of a repeat of the Israeli war here two years ago were palpable.After rockets were fired from a citrus grove behind houses in eastern Gaza City on Tuesday afternoon, the Israelis fired mortar rounds at the source. Three shells landed on a sandy street in front of a home about half a mile from the border, killing three members of the Helou family and a neighbor.

The dead were Yasser Hamed al-Helou, 60, who was just coming out of his garden by the street, his 15-year-old grandson, a 10-year-old relative, and a 17-year-old neighbor, Mohammed Harrara. The boys had been playing soccer, witnesses said.

Two other mortar shells landed behind the house, spreading shrapnel that created fist-size holes in nearby houses. Adham Abu Selmiya, an emergency services spokesman, said the Israeli attack also wounded 10 people, some of them seriously.

Israel’s prime minister, Benjamin Netanyahu, expressed regret at the deaths of civilians, adding, “It is regrettable that Hamas continues to intentionally rain down dozens of rockets on Israeli civilians even as it uses civilians as human shields.”

The Israeli military also said it regretted the loss of civilian life and placed the blame on Hamas. “We do not target civilians,” Lt. Col. Avital Leibovich, a military spokeswoman, said by telephone. “This was not our initiative. It was reactive.”

Colonel Leibovich said the army believed that a militant was also killed in that attack. But there was no evidence of that from the hospital or neighbors.

Relatives and neighbors were unusually open about the fact that the Israeli mortar attack was an attempt to hit militants firing rockets from the nearby grove.

“We heard the sound of four mortars being fired by militants from a grove just beyond our house,” said Hassan, the older brother of Mohammed Harrara. “A few minutes later, the Israeli shells landed in the area.”

Hamas appears to have ended a two-year cease-fire that had held since the three-week Israeli military operation in Gaza ended in early 2009. But it was unclear if policy had shifted; there have been signs of a rift between Hamas’s hard-line military wing and the government, which may have led to the escalation. Hamas statements have said the recent attacks are a response to “ongoing Israeli crimes.”

Abu Obaida, a spokesman for the military wing, told reporters on Tuesday that his men “cannot be deterred” by Israeli attacks.

He said that Hamas respected the cease-fire with Israel and had tried to enforce it, but that “the resistance cannot control itself forever.” He added that if Israel stopped its attacks on Gaza, Hamas would hold back as well.

Overnight on Monday, Israeli F-16s carried out eight airstrikes, hitting a Hamas training camp, a brick factory, a metal workshop and a mechanic’s garage. Local reports said that at least five people, including a woman and two children, sustained moderate injuries.