Mr Bush's statement is the diplomatic highlight of his visit

He also urged a solution to the issue of Palestinian refugees that would involve paying them compensation.

It is thought to be Mr Bush's strongest public statement pressing Israel to give up land it seized in the 1967 war.

He was speaking in Jerusalem following two days of separate talks with Israeli and Palestinian leaders.

He has been trying to encourage the two sides into peace talks, and says he wants a peace deal signed by the time he leaves office in January 2009.

Mr Bush said in a statement: "It is vital that each side understands that satisfying the other's fundamental objectives is key to a successful agreement."

He said this would require:

secure recognised and defensible borders for Israel

a viable, contiguous, sovereign and independent Palestinian state

He added: "Agreement must establish Palestine as a homeland for the Palestinian people just as Israel is a homeland for the Jewish people."

Stern warning

Mr Bush did not give details of precisely what a final agreement might contain - he said that would be a matter for the talks.

But his statement set out some parameters within which he expected negotiators to work.

These included:

Palestinian refugee families should be compensated, rather than returning to former homes in what is now Israel

adjustments to the pre-1967 boundaries "to reflect current realities" - a reference to Israeli settlements in the occupied West Bank

He issued a stern warning to both sides not to do anything which breaks promises they have already made, or which might make negotiations more difficult.

"On the Palestinian side, that includes confronting terrorists and dismantling terrorist infrastructure," he said.

Most recent attacks on Israel have come from inside Gaza, which is run by the Islamic militant group Hamas, and not Mr Abbas.

However, Mr Bush made no direct reference to Gaza in his statement.

And he underlined the US commitment to Israeli security.

Mr Bush goes on to Gulf states on Friday, some of which have been less hostile to Israel than other Arab states. He urged Arab states to reach out to Israel - a step he said was "long overdue".