JERUSALEM—Militants in the Gaza Strip stepped up rocket and mortar attacks into southern Israel, as Palestinian, Israeli and American leaders failed during a second-straight day of negotiations to resolve a dispute over Jewish settlement building that threatens to sink newly launched Mideast peace talks.

Hillary Clinton greets Shimon Peres at the Israeli presidential residence in Jerusalem Wednesday.

.The Obama administration's point man on the peace process, George Mitchell, said there had been significant progress in roughly two hours of meetings Wednesday between Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas on the core issues needing resolution for establishment of an independent Palestinian state.

But the American diplomat said more talks would be required next week between lower-level Israeli and Palestinian officials to keep the process moving beyond a key late-September deadline. Mr. Abbas has threatened to walk out of the talks if Mr. Netanyahu doesn't maintain a construction freeze on Jewish building in the West Bank that Israel says will expire no later than the end of September.

Conservative members of Israel's ruling coalition, meanwhile, have said they would pull their support for Mr. Netanyahu's government if the moratorium is continued.

"That subject [of settlements] was discussed this evening, we continue in our efforts to make progress in that regard and believe that we are doing so," Mr. Mitchell told a Jerusalem press conference on Wednesday night.

Both Palestinian and Israeli officials showed flexibility after the talks, noting that they were still hopeful that a compromise could be reached on the issue.

A Palestinian official said that even though there is still no agreement on their demand for an extended settlement freeze, they are "encouraged" by the intensive U.S. involvement and believe an agreement is possible.

"It is incomprehensible that on the table you discuss ending the occupation, and under the table Israeli bulldozers are expanding the occupation," said Husam Zumlot, a spokesman for the negotiating team. "We want for this U.S.-sponsored process to turn the Israeli bulldozers from destroying homes to building bridges. What is missing is an Israeli De Gaulle."He didn't comment on whether there was any progress in the talks.

U.S. officials have been advising the two sides to directly engage on the most contentious issues concerning the development of a Palestinian state, particularly its future borders, to give the peace process momentum.

Washington has stressed to Mr. Abbas that an agreement on borders removes the significance of Israeli construction in areas expected to be located inside Israel's borders as part of a future peace agreement, according to American diplomats.

"The two leaders are not leaving the tough issues to the end of their discussions; they are tackling up front—and did so this evening—the issues that are at the center of the Israeli-Palestinian conflict," Mr. Mitchell said. Intensified conflict Wednesday between Gaza-based militants and the Israeli military, however, is raising concerns among Israeli and U.S. officials that opponents of the revitalized Middle East peace process could increasingly seek to sabotage the talks through violence.

Israeli officials are particularly eyeing the role of the militant Palestinian organization Hamas, which controls the Gaza Strip and receives significant arms and funding from Iran and Syria.

A spokeswoman for the Israeli Defense Forces said eight mortars fired out of Gaza Wednesday hit near kibbutzim in southern Israel, while a rocket was launched into the city of Ashkelon. It marked the most ordnance fired out of the Gaza Strip in a single day in 18 months. There were no reports of injuries.

"It's definitely an escalation," said an Israeli army spokesman. "We hold Hamas responsible for whatever happens in the strip."

Israel's air force responded by bombing a suspected arms-smuggling route along the Gaza-Egypt border, said the official. No group claimed responsibility for the attacks.

Israeli President Shimon Peres, following a meeting Wednesday with Secretary of State Hillary Clinton, described Israel and the U.S. as in a regional standoff with Iran and its allies, mainly Hamas, Syria and the Lebanese militia Hezbollah.

"I believe all the independent countries in the Middle East feel that they are threatened [by Iran], no matter to which religion or nation they do belong," Mr. Peres said. "It's also a threat, I believe, to the rest of the world."

Hamas's military wing reported on its website Wednesday that one Palestinian was killed and two others were injured by the Israeli strike on the Gaza border. Yesterday, the head of the Hamas military wing, Ahmed Jaberi, encouraged militants to continue an arms struggle against Israel. He criticized the peace talks and said that Israel will be defeated only by force.

Since the beginning of the week, 14 rockets and mortars have been fired into Israel from Gaza, the Israel Defense Forces said Wednesday. More than 150 rockets and mortars have been fired at Israeli territory since the beginning of 2010, it added.

The Obama administration increasingly is seeking broader support from the Arab governments for the peace process, as well as to contain Iran.

Mr. Mitchell will fly to Damascus Thursday to meet with Syrian President Bashar al-Assad and then move on to Beirut to meet Lebanon's president and prime minister Friday.