GAZA CITY, Gaza Strip (AP) — A new round of violence between Israel and Palestinian militants has Gaza’s Hamas rulers caught between reluctance to take on Israel and discomfort with reining in fellow Islamists from smaller, more radical groups involved in the fighting.

The fighting has killed 10 Palestinians and an Israeli, casting doubts on assessments that the recent prisoner swap between Israel and Hamas might improve relations between the bitter foes. Despite the worst bloodshed in months, both sides indicated they were interested in restoring calm.

Hamas, which has ruled Gaza since 2007, has avoided direct involvement in the latest burst of fighting. Hamas lost hundreds of men in a fierce Israeli offensive against rocket squads three years ago and has largely maintained calm since then.

At the same time, the group, which has killed hundreds of Israelis in suicide bombings and other attacks, remains committed to armed struggle against Israel. Threatened by even more radical rivals in Gaza, Hamas has not criticized anyone for attacking Israel.

“The Palestinian resistance has the full right to defend itself against the Zionist crimes against the Gaza Strip,” Mahmoud Zahar, a top Hamas official, told the group’s website.

Most of the violence this weekend has been between Israel and Islamic Jihad, an Iranian-backed group that is considered even more extreme than Hamas. Israel says it holds Hamas responsible for attacks from Gaza, and there is little doubt that Hamas’ control — when it wants to exercise it — is strong.

In the latest violence, an Israeli airstrike hit a pair of militants in Gaza on Sunday as they prepared to fire a rocket into Israel, the military said. Gaza’s Health Ministry said one man was killed and a second was wounded. Just before nightfall, Gaza militants fired another rocket into southern Israel which landed in an open area and caused no injuries or damage, the army said.

In New York, U.N. Secretary-General Ban Ki-moon condemned the rocket fire and urged “maximum Israeli restraint.”

European Union foreign policy chief Catherine Ashton also called for restraint. “I wholeheartedly condemn the indiscriminate targeting of civilians where ever they are,” she said.

The fighting Sunday came a day after eight Palestinian militants and an Israeli civilian were killed. It took place as Egyptian mediators were trying to broker a truce. Egypt, which borders Gaza to the south, brokered this months’ prisoner swap between Israel and Hamas.

That deal has raised speculation that the two enemies might somehow create a working relationship despite their rejection of each other, perhaps with Israel easing its blockade on Gaza. Israel says the closure — which enables basic goods to get in through Israel’s border and does not affect Gaza’s border with Egypt — is needed to halt arms smuggling.

Gaza militants have steadily improved their rocket capabilities in recent years to the point where rocket fire can bring life to a standstill for more than a million people living in a broad area between Israel’s southern border and the outskirts of Tel Aviv. Neither Israel’s invasion in the winter of 2008-2009 nor a new missile defense system have been able to halt the rocket fire.

The rocket attacks — including Saturday’s deadly strike that killed an Israeli man as he traveled in his car — have enraged the public. Reflecting this anger, one prominent Israeli, Haim Ramon, urged the government to topple Hamas.

“The Israeli military can do it,” Ramon, a moderate who held a series of senior Cabinet posts before leaving politics in 2009, told Channel 10 TV.

“A normal country cannot allow that every three months some terrorist … can force 1.5 million people into shelters,” he said.

Hamas seized control of Gaza in 2007.

Israeli defense officials confirmed that there are contingency plans for a broad invasion of Gaza to topple Hamas. But they said this is a worst-case scenario among many options, and the preference is to restore the calm that has largely prevailed since 2009. The officials, speaking on condition of anonymity because they were discussing sensitive military plans, would not say what would trigger an Israeli invasion.

Likewise, Hamas officials signaled that they, too, would like to prevent the violence from spinning out of control.

“We want to keep the Palestinian people away from suffering from war and aggression,” said a senior Hamas official. “But if Israel chooses confrontation, we are ready.”

The Hamas official, speaking on condition of anonymity because he was discussing sensitive internal deliberations, said Hamas was working with Egypt and other Palestinian armed groups “to reach an internal consensus.”

Earlier Sunday, Islamic Jihad said it, too, was open to a cease-fire, but Israel had to go first.

“When all jet fighters leave the skies of Gaza, we will stop firing rockets,” said Dawud Shehab, a senior member of Islamic Jihad.

During the current round of violence, Israel has responded to immediate threats of militants firing mortars or rockets, but has so far stopped short of hitting larger, strategic targets.

The latest round of violence was set off by a rocket attack last Wednesday by Islamic Jihad. The group said that attack was meant to mark the 16th anniversary of the assassination of its founder by Israel.

As a precautionary measure, Israeli officials closed schools near Gaza, as well as Ben-Gurion University in Beersheba, officials said.

In Gaza, senior militants disappeared from the streets and Hamas movement scaled back its police deployment, apparently afraid they would be targeted by Israeli planes.