Bush's visit to Sharm El Sheikh for the gathering of hundreds of world policymakers and business leaders was the final stop on his five-day Middle East trip - seen as a farewell tour - to Egypt, Israel and Saudi Arabia.
But the president's criticism of Hamas, which has been shunned by Israel and the West as a "terrorist organisation" despite winning Palestinian parliamentary elections in 2006, is likely to stir new controversy.
Egypt, a key US ally, has been negotiating indirect talks between Hamas and other Palestinian groups on one side and Israel on the other.
Amani Soliman, Al Jazeera's Middle East editor, said: "For Bush to come out and say this in Egypt ... puts the Egyptians in an uncomfortable situation.
"These people are sitting down to talk to the Israelis, albeit through Egypt."
Before the US president spoke, Hosni Mubarak, the Egyptian leader, had called on Israel to accept peace offers by the various Palestinian factions, stressing that no agreement would be forced on the Palestinians.
Bush also told Arab leaders that the "time had come" to reform their political systems.
He said: "Too often in the Middle East, politics has consisted of one leader in power and the opposition in jail.
"The time has come for nations across the Middle East to abandon these practices, and treat their people with the dignity and respect they deserve."
'Invest in Palestinians'
The US president's trip comes eight months before the end of his presidency - the target date Bush set for reaching a peace agreement that would see the creation of a Palestinian state.
Insisting a deal was still possible before he leaves office, Bush said: "A peace agreement is in the Palestinians' interest, it is in Israel's interest, it is in Arab states' interest, and it is in the world's interest."
He called for Arab nations to seize the opportunity and "invest aggressively in the Palestinian people".
Directing his comments at Palestinian and Israeli leaders, he said: "Palestinians must fight terror and continue to build the institutions of a free and peaceful society. Israel must make tough sacrifices for peace and ease restrictions on Palestinians."