The statement President Bush delivered at the conclusion of his recent meeting with Palestinian President Mahmoud Abbas deserves serious attention. It has been much discussed by the Israeli press but drew scant commentary in the U.S. media. The president, in his formal presentation, declared that any final-status agreement between Palestinians and Israelis "must be reached between the two parties, and changes to the 1949 armistice lines must be mutually agreed to."

Lest there be any misunderstanding, the president said that "Israel should not undertake any activity that contravenes road map obligations or prejudices final-status negotiations with regard to Gaza, the West Bank and Jerusalem. . . . A viable two-state solution must ensure contiguity of the West Bank. And a state of scattered territories will not work. There must also be meaningful linkages between the West Bank and Gaza. This is the position of the United States today. It will be the position of the United States at the time of final-status negotiations."

Bush's declaration was a significant and helpful restatement of some long-held American positions. If these principles are actively embedded in Washington's policies over the months ahead, they could help further the president's stated goals of resolving the long-running Israeli-Palestinian conflict, promoting democracy in the Middle East and undercutting support for Islamist terrorism.

Thirty-eight years ago this month, Israeli forces occupied the Sinai Peninsula, the West Bank (including East Jerusalem) and Gaza, and the Syrian Golan Heights. At the time, and without much discussion, President Lyndon B. Johnson made the decision that Israel should be allowed to hold on to the captured Arab territories until the Arabs were ready to make peace with Israel and offer recognition and security. This "land for peace" principle was later embodied in U.N. Resolution 242 and ever since has formed the touchstone for all considerations of Arab-Israeli peace.

Johnson, while very supportive of Israel, went on record as saying that the future borders of Israel "should not reflect the weight of conquest" and that any adjustments to the borders that prevailed before the June 1967 war should be small and mutually agreed to. Since those foundational statements on the territorial aspect of a peace settlement, U.S. policy under successive presidents did not change in any significant way until last year.

Then, in a letter to Ariel Sharon in April 2004, Bush seemed to accept the Sharon government's position that new "facts on the ground" -- namely Israeli settlements in the West Bank -- made it unrealistic to think that Israel should ever withdraw to the old armistice lines of 1949. He said then that "it is unrealistic to expect that the outcome of final-status negotiations will be a full and complete return to the armistice lines of 1949." (Bush also stated that Palestinian refugees should not expect to return to Israel proper as part of any peace settlement.) The Bush letter was widely seen as a triumph for Sharon. For the first time, an American president had openly sided with the current Israeli view that the passage of time and new realities obviated Israel's obligation to withdraw more or less to the 1967 lines (essentially the same as the 1949 armistice lines) in return for peace, recognition and security.

The president's recent elaboration of U.S. policy is essentially a reaffirmation of the traditional American view that the 1949 armistice lines should be the starting point for any discussion of border changes and that changes in them cannot be one-sided. Much like his predecessors, the president also said last month that "Israel must continue to take steps toward a peaceful future and work with the Palestinian leadership to improve the daily lives of Palestinians, especially their humanitarian situation."

The question inevitably arises of whether the president meant what he said and how in practice he can reconcile his commitment to Sharon with the May 26 statement. We will have an early clue when Secretary of State Condoleezza Rice visits the area next week. Will she reaffirm what the president said about the 1949 lines (including Jerusalem) and the need for mutual agreement for any changes in them? So far we have few indications that the Bush administration has decided to make the kind of commitment that would be needed.

Yet the president has a clear incentive to make that effort, and were he to do so he could count on broad bipartisan support from the American public. All of his ambitious and valuable goals in the Middle East would be helped immeasurably by a successful conclusion of Israeli-Palestinian peace negotiations.

For the next few months the Israeli-Palestinian agenda is likely to be dominated by the impending Israeli withdrawal from Gaza and by Palestinian elections. But before year-end the moment of truth for the Bush administration will arrive, and the president will have to decide whether to live up to the words he spoke last month by injecting a sense of urgency into the search for a final-status Israeli-Palestinian peace, or whether to settle for another interim agreement, as preferred by Sharon.

We both worked with a president -- Jimmy Carter -- who decided to go all out to achieve Israeli-Egyptian peace. We also know that any major American peace initiative in the Middle East can be politically costly and immensely time-consuming. Yet without a truly serious U.S. initiative, the parties will never reach a fair and lasting peace. In terms of the American national interest, exercising presidential leadership was the right thing to do in 1978-79, and it is the right thing to do in 2005.

Zbigniew Brzezinski was national security adviser to President Jimmy Carter, and William B. Quandt was a senior member of his staff with responsibility for the Middle East.