The Israeli and Egyptian leaders have held a rare meeting to co-ordinate preparations for a regional conference due to be hosted by the US next week.
Olmert and Murbarak met at Sharm el-Sheik on the Red Sea
Israeli PM Ehud Olmert told reporters he hoped a peace deal with the Palestinians could be reached in 2008.
The Sharm el-Sheikh summit comes a day after he failed to bridge gaps with Palestinian leader Mahmoud Abbas over a agreed blueprint for future talks.
Egypt's President Hosni Mubarak offered to travel to Israel if that would help.
A joint declaration about final status negotiations between Israel and the Palestinian had been intended to be the centrepiece of the next week's Annapolis conference in the US.
A senior Palestinian negotiator, Saeb Erekat, said the two sides would continue their efforts on Tuesday to try to agree a text.
Analysts say that without a joint Israeli and Palestinian statement, the conference will have little chance of success.
Mr Olmert went a little further than his previous prediction that an Israeli-Palestinian peace deal could be reached before US President George W Bush leaves office in January 2009.
"The negotiations will not be simple. There will be differences, crises and arguments. But if we act with caution, there is a chance that we can reach a deal," he said.
A major problem will be solving the split between the West Bank and Gaza Strip, which the militant group Hamas took control of in June.
"Gaza must be part of the Palestinian state and then, naturally, the Palestinians must fight terrorism, and that includes the Gaza Strip," Mr Olmert said.
Mr Mubarak said he would be prepared to re-enact his predecessor Anwar Sadat's ground-breaking trip to Jerusalem, which took place exactly 30 years ago on Monday.
"If my visit to Israel will solve the Palestinian problem, I'm ready to go," Mr Mubarak said in response to a journalist's question at the Sinai resort.
The veteran Egyptian leader has visited Israel, for assassinated Prime Minister Yitzhak Rabin's funeral in 1995, but it was an unofficial visit.
Israel and the US have been pressing for high level Arab representation at the Annapolis talks due next week.
Arab foreign ministers are meeting in Cairo on Friday to coordinate their positions, although each government is to decide separately whether to send a delegation.
Egyptian officials say they are convinced the US is now committed to launching a serious peace process and its foreign minister is expected to attend.
Analysts say other Arab states, including Saudi Arabia, believe Israel has not offered enough assurances about its seriousness to reach peace and to make the necessary sacrifices.
Israel and the Palestinians are divided over the fate of the West Bank, Gaza, and east Jerusalem, occupied by Israel since 1967, and the Palestinian refugee problem dating back to the establishment of Israel in 1948.
Syria has said it will only join the conference if the issue of the Golan Heights, also occupied by Israel in 1967, is on the agenda.