JERUSALEM - Israel's government came under mounting pressure Thursday to oust Gaza's Hamas rulers after a rocket fired from Gaza hit a medical clinic in an Israeli shopping mall and seriously wounded four people, including a 2-year-old girl.

Israel's intelligence chief warned that within two years, Hamas would be able to extend the range of its rockets to 25 miles (40 kilometers) and put more Israeli cities at risk. Wednesday's Grad rocket, which Israeli security officials said was made in Iran, hit the coastal city of Ashkelon, about 15 kilometers (nine miles) from Gaza.

Prime Minister Ehud Olmert has held off for now on ordering a major military offensive in Gaza, in part because Israel would not have a clear exit strategy and because the fighting would likely bring peace talks with the moderate Palestinian government in the West Bank to a halt.

However, rocket fire has intensified in recent days, with two Israelis killed in separate attacks on Friday and Monday. Wednesday's attack on a crowded mall in one of Israel's largest cities highlighted the vulnerability of Israeli civilians.

The rocket was fired just after visiting U.S. President George W. Bush and Olmert discussed the violence across the Gaza-Israel border. Speaking at a world conference marking Israel's 60th anniversary Wednesday, Olmert said Israel will take the "necessary steps" to stop violence from Gaza and called the Ashkelon attack "intolerable and unacceptable."

"The government of Israel is committed to stop it," he said.

The rocket ripped through the roof of the mall, causing a large chunk of the roof to collapse in a huge pile of rubble and twisted metal, hitting the clinic. Four windows were blown out of the side of the building.

A 55-year-old female doctor was seriously wounded by shrapnel, said Leah Malul, spokeswoman of Ashkelon's Barzilai Hospital. A 24-year-old woman and her 2-year-old daughter suffered serious head wounds, and a 25-year-old woman was seriously wounded in the abdomen, said Malul. Eleven others were lightly hurt, and dozens suffered from shock.

Liron Azulai, 26, an electronics student, was in the third-floor clinic when the rocket struck. "The whole ceiling fell on me," he said while awaiting treatment at the hospital. He said Israel's government must take action to stop the rocket attacks. "You cannot live like this," he said. "It's very frightening."

Two small Palestinian militant groups claimed responsibility for the attack, though Israel held Gaza's Hamas rulers and their Iranian supporters responsible. Israel views Iran as a major supplier of rockets being smuggled into Gaza through tunnels under the Gaza-Egypt border.

"We are at war with the state of Hamas-stan and this state has to cease to exist," Israeli Vice Premier Haim Ramon said Thursday, though he stopped short of calling for a ground offensive. Such a campaign would likely lead to many casualties on both sides and offer no guarantee of success. Fighting in densely populated Gaza has proven to be extremely complicated, and Hamas' military strength has grown in recent years.

Israel's intelligence chief, Amos Yadlin, told the Haaretz daily that by 2010, Hamas would likely be able to extend its rocket range to 25 miles (40 kilometers), meaning Israeli cities such as Beersheba and Ashdod would also come within reach.

"If this matter is not dealt with, Hamas will bring more cities within its range of fire," Yadlin said.

On Wednesday, the Israeli military commander, Lt. Gen. Gabi Ashkenazi, changed his stand and came out in favor of a ground offensive, defense officials said. They spoke on condition of anonymity because they were not at liberty to disclose policy considerations.

Israel's high-tech military has been unable to find a way to stop the crude rockets. Past invasions have halted daily rocket fire only briefly, and the barrages resumed as soon as Israeli troops pulled out.

In parallel, Egypt has been working to mediate a truce between Israel and Hamas. In a rare hint that Israel might accept it, Olmert referred to "possible terms in what may emerge as a cease-fire" in his talks with a high-level Egyptian mediator.

Before he leaves office, Bush hopes to broker a peace agreement between Israel and the moderate Palestinian government of President Mahmoud Abbas in the West Bank.

Israel has warned it will not carry out any peace agreement until Abbas regains control of Gaza. Hamas seized control of Gaza last June from Abbas' troops.

Abbas claims the West Bank and Gaza - areas located on opposite sides of Israel - for a future independent state. Hamas, an Islamic militant group committed to Israel's destruction, opposes the peace talks.

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Additional reporting by Ian Deitch in Jerusalem.