In a press conference, Bush said Iraq's government "isn't perfect" but "progress" was being made on political reconciliation.
He called for Arab leaders to get behind Fouad Siniora, Lebanon's prime minister, and said that "nations in the neighbourhood" were willing to help Israelis and Palestinians reach a peace deal.
Mubarak endorsed US hopes for an Israeli-Palestinian peace plan concluding before the end of 2008, and said he will work hand-in-hand with the US and other nations.
Bush urged greater political openness in Egypt, but did not directly criticise the Egyptian government for what the US has previously noted as a lack of political freedoms.
"I'm absolutely confident that people in the Middle East are working on building a society based on justice," Bush said.
Bush has been on an eight-day tour of the Middle East to gather Arab support both for his goal of reaching an Israeli-Palestinian peace deal by the time he leaves office in January 2009 as well as in Washington's stand-off with Iran.
Relations with Egypt have taken a downturn over Washington's criticism of Cairo's perceived failure to secure its border with the Gaza Strip, now run by the Hamas movement, regarded as a "terror group" by Israel and the West.
Bush flew in from Saudi Arabia after having breakfast with members of the royal family at a ranch belonging to close ally King Abdullah outside Riyadh.
The US president used his two-day visit to the world's biggest oil producer to press for increased output to help ease recession fears at home, saying the "very high" prices were tough on the US economy.
OPEC is due to meet in Vienna on February 1 under pressure to calm prices which hit $100 a barrel at the start of the year.
But Bush faced difficulty in convincing his Saudi hosts to wholeheartedly support the twin pillars of his tour -- greater backing for the Middle East peace process and a willingness to confront the "threat" of Iran.
Saud al-Faisal, the Saudi foreign minister, gave a cool response to Bush's call for Arab countries "reach out" to Israel, which only has signed peace treaties with Egypt and Jordan.
"I don't know what more outreach we can give to the Israelis," he told a press conference with Condoleezza Rice, the US secretary of state.
On Iran, al-Faisal said: "Iran is a neighbouring country, an important country in the region. Naturally we have nothing bad against Iran."
Saudi Arabia, like other Gulf states, is determined to avoid further conflict after the 2003 US-led invasion of Iraq, which served to strengthen the regime in the Islamic republic.
Bush reiterated his warning that "all options are on the table" over Iran, and said he had asked King Abdullah and other Gulf leaders to do more to pressure the Islamic republic over its contested nuclear programme.