Israeli and Palestinian leaders are delving very quickly into some of the most difficult issues dividing them, the U.S. special envoy to the region said in an unusually upbeat report Wednesday, even as Israeli fighters bombed a smuggling tunnel and Palestinian militants launched mortar rounds into southern Israel.

Israeli Prime Minister Binyamin Netanyahu greeted Palestinian Authority President Mahmoud Abbas at his Jerusalem residence, with a Palestinian flag as a backdrop, for two hours of talks that also included Secretary of State Hillary Rodham Clinton and U.S. special envoy George J. Mitchell. The two leaders had met in Egypt for more than two hours Tuesday, also accompanied by Clinton and Mitchell.

"They are serious, they mean business," Mitchell told reporters afterward. "I will say that the two leaders are not leaving the tough issues to the end of their discussions," he said. "We take this as a strong indicator of their belief that peace is possible."

The talks have been greeted with deep skepticism in Israel and the Arab world, with few appearing to think that the two sides can reach an agreement that can be implemented, especially with the militant group Hamas controlling the Gaza Strip, where 40 percent of Palestinians in the territories live. The talks also face a looming crisis with the Sept. 26 expiration of a partial moratorium on Jewish settlement construction.

Palestinian officials insist they will walk out of the talks if settlement construction begins anew, and Mitchell refused to say Wednesday whether the United States was confident the Palestinians would keep talking. "That subject was discussed this evening. We continue in our efforts to make progress in that regard and believe that we are doing so," he said.

Mitchell noted that talking about delicate issues - which could include borders, security, the status of Jerusalem and the right of Palestinians to return to their homes - was not the same thing as negotiating solutions. But he positively compared the experience of the past two days to his work as peace envoy in the Northern Ireland conflict. Then, he said, it was months before the difficult topics were addressed. In the current talks, he said, "it has been literally days."

The Obama administration is pressing for the peace talks to be concluded within a year. Officials are also seeking a comprehensive peace between Israel and its other Arab neighbors, and Mitchell will travel Thursday to Syria and Lebanon for talks. Netanyahu had been cool to talks with Damascus, but there are signs that Syria and Israel are inching toward discussions, including virtual silence from the Syrian government about the resumption of Israeli-Palestinian talks.

"We do not believe that proceeding on both tracks is mutually exclusive," Mitchell said. "To the contrary, we believe they can be complementary and mutually beneficial."

Abbas had come close to a deal with Netanyahu's predecessor, Ehud Olmert, but this was his first visit to the prime minister's residence since Netanyahu took power 18 months ago. The visit represents a calculated risk that Palestinians will not view him as weak for not insisting on meeting on neutral ground.

Also Wednesday, the Israeli military said it had struck a Hamas-operated tunnel on the border with Egypt, asserting that it was used in attacks against Israelis. Local media reports said one Palestinian was killed. The military also said one Qassam rocket and eight mortar shells had hit southern Israel, the largest number of projectiles fired from the Gaza Strip in a single day since March 2009.