LOS ANGELES — Prime Minister Blair called for a rethinking of foreign policy toward the Middle East yesterday, warning that the American-led “war on terror” risked alienating mainstream Arab opinion.

He said “a complete renaissance of our strategy” was needed to fight “an arc of extremism stretching across the Middle East.”

Mr. Blair said the West was engaged in an “elemental struggle that will shape our future” but that it could not be resolved by force alone. Unless the West reappraised its strategy, revitalized the global agenda on poverty and climate change, and resolved to “bend every sinew of our will to making peace between Israel and Palestine, we will not win.”

Mr. Blair said the battle of ideas must be joined to make sure the forces of moderate Islam prevailed over reactionary and terrorist elements.

“We will not win the battle against this global extremism unless we win it at the level of values as much as force — unless we show we are even-handed, fair, and just in our application of those values to the world,” he told a 2,000-strong audience at the World Affairs Council in Los Angeles.

Downing Street denied that the speech amounted to an admission that the Iraq war had been a mistake. But it was an acknowledgement that there had to be a much stronger effort to convince moderate Muslims that the West was committed to resolving the conflict between Israel and the Palestinian Arabs.

His speech will be seen as an implicit criticism of President Bush’s insistence on using military force to crush militant Muslims and of the way the “road map” for the Middle East has been put on the back burner.

Mr. Bush has refused to push Israel into a cease-fire because he says the conflict is an opportunity to defeat Hezbollah, which is supported by Syria and Iran.

Mr. Blair’s admission that force alone was not enough may be seen as an attempt to stem growing dissent in the British Cabinet. He has faced accusations that he is Mr. Bush’s poodle for refusing to call for an immediate Israeli cease-fire.

It also emerged that more than the three known Cabinet “doubters” had signaled to Mr. Blair their unease over his failure to seek such a cessation. The secretary of the environment, David Miliband, the House of Commons leader, Jack Straw, and the international development secretary, Hilary Benn, have raised their concerns. But at a Cabinet meeting last week, one or more other ministers reportedly passed notes to Mr. Blair saying their silence should not be taken as consent.

Downing Street insisted last night that Mr. Blair had not changed his view of the Lebanon crisis and firmly believed that any lasting cease-fire must be agreed upon by both sides.

The foreign secretary, Margaret Beckett, blocked moves by the European Union on Monday night to urge an immediate cease-fire, despite speculation of a rift with Mr. Blair over the crisis.

Mrs. Beckett, privately believed by some colleagues to be out of her depth, refused to back the cease-fire call from fellow foreign ministers in Brussels.

Apparently aided by Germany and the Czech Republic, she endorsed a compromise statement advocating an “immediate cessation of hostilities” leading to a “sustainable cease-fire.”

Mrs. Beckett indicated afterward that what mattered was a sustainable solution to the crisis, publicly echoing Mr. Blair’s approach, which is increasingly enraging members of Parliament in the Labour Party.

She said, “There are a number of colleagues who said that what we want is something that can be sustained. What no one wants is to see violence stop and then break out again immediately.”

But friends of Mrs. Beckett, who has only been the foreign secretary since May, say she is increasingly frustrated that Mr. Blair has not openly condemned Israeli attacks, despite the rising death toll among Lebanese civilians.

Mr. Blair told his American audience that the purpose of Hezbollah’s provocation that began the conflict was to create “chaos, division, and bloodshed to provoke retaliation by Israel that would lead to Arab and Muslim opinion being inflamed, not against those who started the aggression, but against those who responded to it.”