Israel's Prime Minister Ehud Olmert has said failure to negotiate a two-state solution with the Palestinians would spell the end of the State of Israel.
Mr Bush wants a Middle East peace deal by the end of 2008
He warned of a "South African-style struggle" which Israel would lose if a Palestinian state was not established.
Mr Olmert was returning from the Annapolis conference in the US where he and Palestinian leader Mahmoud Abbas pledged to launch formal peace talks.
The two leaders set a goal of reaching a peace deal with US support in 2008.
US President George W Bush called Annapolis, the first substantive Arab-Israeli peace talks in seven years, a "hopeful beginning" for Mid-East peace.
Mr Olmert said it was not the first time he had articulated his fears about the demographic threat to Israel as a Jewish state from a faster growing Palestinian population.
He made similar comments in 2003 when justifying the failed strategy of unilateral withdrawals from Israeli-occupied land which holds large Palestinian populations.
"If the day comes when the two-state solution collapses, and we face a South African-style struggle for equal voting rights, then, as soon as that happens, the State of Israel is finished," Mr Olmert is quoted saying in Haaretz newspaper.
After the ceremonies at Annapolis and the White House, the US appointed former Nato commander Gen James Jones as its new Middle East envoy.
Among his tasks will be to monitor how the Israelis and Palestinians live up to the security commitments made under the relaunched international peace plan known as the roadmap, which forms the basis for the negotiations.
"Building security in the Middle East is the surest path to making peace in the Middle East," US Secretary of State Condoleezza Rice said of his appointment.
"Gen Jones is the best individual to lead our efforts in this essential endeavour."
Mr Bush promised to use American power "to help you as you come up with the necessary decisions to lay out a Palestinian state that will live side-by-side in peace with Israel".
According to the agreement, the Israeli and Palestinian leaders will meet every other week and teams of negotiators led by a joint steering committee will meet on 12 December.
Last year's Palestinian parliamentary election winner Hamas - which does not recognise Israel and has been shunned by the US and Israel as a terrorist organisation - immediately rejected Annapolis as a "failure".
There have been angry protests in the Gaza Strip, controlled by Hamas, and the West Bank since the summit.
Expectations had been low as representatives of more than 40 countries and international agencies gathered in Annapolis ahead of Tuesday's conference.
But in a joint statement concluded with only minutes to spare before the conference formally opened, the two sides agreed to launch negotiations for a treaty "resolving all outstanding issues, including all core issues without exception".
Both sides have said those "core issues" will include the thorny so-called "final-status issues" - the future of Jerusalem, borders, water, refugees and settlements - which have scuppered previous attempts at a peace deal.