Gaza militants opposed to peace with Israel have threatened to derail the fledgling negotiations, and the Israeli military said eight mortars and one rocket hit Israel by mid-afternoon on the day of the talks — the highest daily total since March 2009. There were no injuries.
Israeli warplanes responded by bombing a smuggling tunnel along the Gaza-Egypt border, the military said. Hamas officials said one person was killed and four wounded.
In Jerusalem, little more than an hour's drive from Gaza, Clinton said Israeli and Palestinian leaders were "getting down to business" on the major issues dividing them, though there was no sign they were any closer to resolving a looming crisis over Israeli West Bank settlements.
The American secretary of state was in Jerusalem for a second day of talks aimed in part at ending the impasse, a day after meeting Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas at a summit hosted by Egypt.
"They are getting down to business and they have begun to grapple with the core issues that can only be resolved through face-to-face negotiations," Clinton told reporters. "I believe they are serious about reaching an agreement that results in two states living side by side in peace and security." Abbas has threatened to walk out of the talks if Israel resumes construction in the settlements after a 10-month slowdown expires at the end of the month. Clinton and President Barack Obama have called on Netanyahu to extend the slowdown.
Netanyahu has signaled he is looking for a compromise.
Earlier this week, he said the current curbs won't remain in place after the end of this month, though he will continue to restrict building activity to some extent.
The Palestinians oppose the settlements because they eat up land they want for their future state. Some 300,000 Israelis live scattered among the West Bank's 2.5 million Palestinians. An additional 200,000 Israelis live in east Jerusalem, the section of the holy city the Palestinians claim as their capital.
President Barack Obama has made his pursuit of a Mideast settlement a centerpiece of his foreign policy. After months of US shuttle diplomacy, he summoned the Israeli and Palestinian leaders to Washington early this month to formally launch the first direct negotiations since talks collapsed in 2008 following Israel's military offensive in Gaza. Obama hopes to forge a deal within a year.
Negotiators will have to tackle a series of issues that have undermined talks in the past: the location of the border between Israel and a future Palestinian state, the fate of Palestinian refugees and the competing claims to the holy city of Jerusalem.
But they will have a hard time addressing those disputes if they cannot resolve the disagreement on the settlement slowdown.
Under intense international pressure, Netanyahu declared curbs on West Bank settlement construction last November, seeking to draw the Palestinians back to the negotiating table. At the time the Palestinians dismissed the move as insignificant, an irony Clinton pointed out ahead of Tuesday's talks in Egypt.
"Now we're told that negotiations cannot continue unless something that was viewed as being inadequate continues," she said.
The slowdown is set to expire on Sept. 26, and Netanyahu is being pressed by many of his religious and nationalist allies in Israel's coalition government to resume construction. Members of his own Likud Party have taken out ads in Israeli dailies in recent days demanding an end to the slowdown.
Both Netanyahu and Abbas share a common enemy: Hamas. The Islamic group took over Gaza in 2007 after ousting Abbas' forces, and it has threatened to unleash new violence as the peace talks move forward.
Following Wednesday's airstrike, Hamas said its security forces had evacuated their installations in preparation for further Israeli retaliation.
A senior Israeli military officer forecast further violence in the coming days.
The officer, speaking on condition of anonymity under military guidelines, said Hamas has become increasingly involved in the violence, turning a blind eye to the attacks and occasionally giving its permission to "proxies" to carry out violence.
Hamas has largely refrained from directly carrying out attacks since a devastating Israeli offensive early last year, and has at times even reined in other armed groups from attacking. But with the resumption of peace talks, the militant group has threatened to change its policy.
Early this week, the head of Israel's Shin Bet security agency warned that Hamas would try to torpedo the new talks, and when negotiations were officially launched early this month, Hamas militants killed four Israelis in the West Bank.
