SHARM EL-SHEIK, Egypt (CNN) -- Egyptian President Hosni Mubarak on Wednesday signed on to President Bush's goal of reaching a Mideast peace deal by the time the U.S. leader leaves office in January 2009.
Mubarak said it was time to "put an end to this Israeli-Palestinian conflict to open new horizons for the Middle East for a more peaceful and secure future."
Bush used the final stop of his six-nation tour of the region to update Mubarak on the Israeli-Palestinian peace talks and Iraq.
Following their meeting, Bush told reporters that "nations in the neighborhood are willing" to help Israelis and Palestinians reach a peace agreement.
One of the stated goals of Bush's trip was to garner support for the Mideast peace process from Arab allies. See Bush's itinerary »
"When I say I'm coming back to stay engaged, I mean it," said Bush, who added he'll return to the region in May. "When I say I'm optimistic we can get a deal done, I mean what I'm saying."
Israel's military, under pressure to respond to ongoing attacks from Gaza, has clamped down on the Hamas-controlled Palestinian territory to push militants away from the Gaza-Israeli border.
With violence as a backdrop, Palestinian and Israeli delegations began discussions this week about so-called core issues in their conflict, including Israeli settlements in the West Bank, the right of Palestinian refugees to return to Israel and Jerusalem as the shared capital of a future Palestinian state. Watch Bush end his Middle East trip »
During his four-hour stop Wednesday in Egypt, Bush said he and Mubarak also discussed the situation in Lebanon, and they agreed there should be an election for president under the Lebanese constitution.
Lebanon has been in the midst of a political crisis as pro- and anti-Syrian lawmakers in parliament are locked in a battle to elect a new president.
Bush said he had a "great trip" during his Mideast tour and called the region a "dynamic part of the world that is seeing significant changes" leading toward a "modern, global economy," while "not abandoning their traditions and their cultures or their faith. It isn't easy work ... and it's going to require social, economic and political reform."
"I'm absolutely confident that the people of the Middle East are working hard to build a society based upon justice," he said. "And I've assured them as they make the journey, the United States will be their friend and partner."
Bush also talked about the Iraq war, saying the nation's fractured government "isn't perfect, but nevertheless progress is being made" on political reconciliation.
Making a surprise visit Tuesday to Baghdad, U.S. Secretary of State Condoleezza Rice congratulated the Iraqi prime minister on the parliament's passage of a measure easing restrictions on former members of Saddam Hussein's Baath Party.
Bush said Rice told him the situation in Iraq is improving and that "she was able to see life returning back to the streets."
Mubarak and the U.S. president took no questions from reporters during their brief joint statements in the Egyptian resort area of Sharm el-Sheik -- Bush's final stop before boarding Air Force One and heading back to Washington.
Earlier on his Mideast tour, the president also visited Israel, the West Bank, Bahrain, Kuwait, the United Arab Emirates and Saudi Arabia.
In the oil-rich kingdom, Bush appealed to the Saudis to boost oil production and help the U.S. economy. Saudi Arabia is one of the key members of the OPEC oil cartel.
Oil prices have peaked at $100 a barrel and are hovering just below triple digits, adding to fears that historically high fuel prices could help push the U.S. economy into recession.
"Oil prices are very high, which is tough on our economy," Bush said Tuesday.
"I would hope, as OPEC considers different production levels, that they understand that if ... one of their biggest consumers' economy suffers, it will mean less purchases, less gas and oil sold." Watch more on Bush's visit »
In response, Ali al-Naimi, the kingdom's minister of petroleum and mineral resources, later said that Saudi Arabia "will raise production when the market justifies it." Al-Naimi said Saudi policy aims "hopefully [to] keep supply matching demand with minimum volatility in the international oil market."
While in Saudi Arabia, Bush also issued a stern warning to Iran in the wake of a January 6 confrontation between U.S. Navy and Iranian vessels in the Strait of Hormuz.
"So the Iranians ... better be careful and not be provocative and get out there and cause an incident," Bush told reporters. "Because there's going to be serious consequences. What I said in my statement was, if they hit one of our ships there's going to be serious consequences. And I meant it."
The Bush administration this week announced a proposed weapons sale to Saudi Arabia as part of a Persian Gulf security strategy to counter threats posed by Iran's rising influence in the region. Watch more on the proposed deal »
The $20 billion arms deal includes the sale of 900 "joint direct attack munitions" worth close to $120 million, said U.S. State Department spokesman Sean McCormack. E-mail to a friend