Bush said "Palestinians and Israelis each understand that helping the other to realise their aspirations is the key to realising their own, and both require an independent, democratic, viable Palestinian state".
"Such a state will provide Palestinians with the chance to lead lives of freedom, purpose and dignity. And such a state will help provide Israelis with something they have been seeking for generations: to live in peace with their neighbours."
Bush said the Palestinians must improve security and stability in their territories and called for an end to Israeli settlement expansion.
But he did not mention the most intractable issues of borders, the final status of Jerusalem and refugees' right of return.
Neither the Palestinians nor the Israelis have indicated they would budge from their positions on those points.
Bush told delegates from more than 50 countries and organisations: "In light of recent developments, some have suggested that now is not the right time to pursue peace. I disagree.
|Many commentators expect little to come out|
of Annapolis beyond the handshakes [AFP]
"I believe that now is precisely the right time to begin these negotiations - for a number of reasons."
He said: "The time is right because a battle is under way for the future of the Middle East - and we must not cede victory to the extremists."
And in remarks that struck a sensitive Palestinian nerve, Bush said "the United States will keep its commitment to the security of Israel as a Jewish state and homeland for the Jewish people".
"This settlement will establish Palestine as the Palestinian homeland, just as Israel is the homeland for the Jewish people."
He was followed at the podium in the memorial hall of the naval academy by Abbas and Olmert.
Abbas laid out some core issues in his speech.
"Tomorrow, we have to start comprehensive and deep negotiations on all issues of final status, including Jerusalem, refugees, borders, settlements, water and security and others," he said.
He expressed the Palestinians' desire for East Jerusalem to be the capital of "our state".
Abbas said: "The exceptional opportunity that the Arab, Islamic and international prescience brings us today coupled with overwhelming Palestinian and Israeli public opinion in support of Annapolis, must be seized in order to be a launching pad for a negotiations process."
Olmert, for his part, reached out to Arab delegates by using the Arabic phrase for "welcome".
"I have no doubt that the reality created in our region in 1967 will change significantly," he said.
"While this will be an extremely difficult process for many of us, it is nevertheless inevitable. I know it. Many of my people know it. We are ready for it."
Olmert said: "We want peace. We demand an end to terror, incitement and hatred. We are willing to make a painful compromise, rife with risks, in order to realise these aspirations."
He did not mentioned the issue of Jewish West Bank settlement building.
In Gaza, thousands of Palestinians staged a protest against the talks on Tuesday.
Ismail Haniya, the Hamas leader and deposed Palestinian prime minister, said Abbas had gone to Annapolis without any support from his people and had no mandate to agree to anything to do with Palestinians' rights.
Bush has made clear that while he was happy to play cheerleader at the conference, he saw the US only as a facilitator and monitor, saying it was up to the Israelis and the Palestinians themselves to move the process forward.
Al Jazeera correspondent Rob Reynolds said, in what could be interpreted as a symbol of how deep his commitment to the process really is, the US president did not stay for the rest of the conference, leaving Annapolis as soon as the speeches were over.