US President George Bush held out the prospect of a homeland to Palestinians last night - but only if they turn from terrorism to democracy.

Mr Bush said there was a great chance for the new state following the death of PLO leader Yasser Arafat.

The newly re-elected President even suggested it could be founded while he was still in the White House.

But he made it clear that progress depends on who is elected as the new Palestinian leader and ruled out an international conference for peace until it was clear progress would be made.

With the Prime Minister looking on, Mr Bush also said US and British troops could face worse violence in Iraq over coming months.

Mr Blair later said Mr Bush had offered the Palestinians a "perfectly fair deal".

However, declarations from the White House summit fell short of what some, including many Labour MPs, had hoped for.

Sir Menzies Campbell, Liberal Democrat foreign affairs spokesman, said "warm words and fine sentiment" would not bring peace.

Mr Blair was the first foreign leader to meet Mr Bush since his election victory last week.

With his close ties to the President a source of friction at home, Mr Blair was facing pressure for progress on the Arab-Israeli conflict, intensified by Mr Arafat's death on Thursday.

But with no international conference and no new US envoy to the Middle East, the Prime Minister faced questions in TV interviews over what he had achieved.

"Anyone who saw the press conference today would not think this was a President who was indifferent to the peace process," he replied.

Earlier, Mr Bush had said: "We have a great chance to establish a Palestinian state and I intend to use the next four years to expend the capital of the United States on such a state. I believe it is in the interests of the world."

He sent his sympathies to the Palestinian people but said Mr Arafat's death meant a new opportunity towards a lasting peace.

He said: "I look forward to working with a Palestinian leadership that is committed to fighting terror and committed to the cause of democratic reform.

"We will also work with Israeli and Palestinian leaders to complete the disengagement plan from Gaza and part of the West Bank.

"These steps, if successful, will lay the foundations for implementing the road map and then lead to final status negotiations."

The summit came as Mr Arafat was buried in the Ramallah complex on the West Bank, where he was kept a virtual prisoner for two-and-a-half years.

Mr Blair said: "We meet at a crucial time where it is important that we revitalise and reinvigorate the search for a genuine, lasting and just peace in the Middle East."

The Prime Minister set out a series of steps towards a two-state solution but said it would not be possible unless both sides were democratic and respected human rights.

On Iraq, Mr Bush warned that the violence in Iraq could get worse in the run-up to elections in January.

"As those elections draw near, the desperation of the killers will grow and the violence could escalate," he said.

Asked about the warning, Mr Blair claimed it had "passed me by".

The President sought to reach out to Europe following the rifts over Iraq, saying they must remain close partners.

He welcomed the enlargement of the EU and vowed to strengthen transatlantic ties in his second term, visiting Europe as soon as possible after his inauguration.

On Iran, both he and Mr Blair said the whole international community was opposed to the country becoming a nuclear power.

However, the Prime Minister did not say whether Britain would back US military action to prevent it.