Egyptian President Hosny Mubarak and Israeli Defence Minister Ehud Barak met in the Sinai resort city of Sharm el-Sheikh on Wednesday, DPA reported.
Ahead of the talks, officials from Mubarak's office said the two were expected to discuss efforts to restart stalled Israeli- Palestinian peace talks following US Mideast envoy George Mitchell's trip to the region last week.
Egypt has, for months, been brokering efforts to bring Israelis and Palestinians back to the negotiating table. It has also sought to reconcile rival Palestinian factions Hamas, which controls the Gaza Strip, and Fatah, which controls Palestinian-administered areas of the West Bank.
Barak, the head of Israel's Labour Party, has said a failure to come to a peace deal based on a two-state solution posed a greater threat to Israel than an "Iranian bomb."
"Any other situation ... is the most serious threat to Israel's future," Barak said Tuesday.
In a similar vein, Egypt has repeatedly warned of the dangers of Iran and Israel's nuclear programmes, and has called for a Middle East free of nuclear weapons.
"All the attention the international community is giving to the Iranian programme must take into account a similar approach to Israel's nuclear capabilities," Israeli Army Radio on Tuesday night quoted Mubarak as saying.
The United States has sought to coax Palestinian President Mahmoud Abbas back to the negotiating table. Abbas has said that he believes there is "no point" in negotiating until Israel stops expanding settlements in the West Bank and East Jerusalem.
Egyptian Foreign Ministry officials on Wednesday told the German Press Agency dpa that Egypt is asking the United States to give Abbas guarantees that it supports a Palestinian state along the 1967 borders, and that East Jerusalem, which Israel annexed after the 1967 war, be recognized as the Palestinian capital.
The two would also discuss the blockade of the Gaza Strip, maintained by both countries since Hamas took control of the territory's security forces nearly three years ago, and Egyptian- brokered talks on a prisoner-swap deal between Hamas and Israel, according to Egypt's official MENA news agency.
Israeli officials have linked the closure of Gaza's borders to a prisoner-swap deal that could see hundreds of Palestinian prisoners freed in exchange for the release of Gilad Shalit, an Israeli soldier captured near the Gaza border in 2006.
Egyptian and German-brokered negotiations on such a deal stalled again at the end of last year.
Relations between Hamas and Egypt have further deteriorated in recent weeks following reports that Egypt is building an underground steel wall along its border with the Gaza Strip to curtail cross- border smuggling through tunnels.
Egypt has never explicitly confirmed it is building such a barrier, but Mubarak this week defended "fortifications along (Egypt's) eastern border" as a matter of "national sovereignty," and "national security," saying they were not open to debate.