Visiting British Prime Minister Tony Blair on Tuesday vowed to continue the war on terrorism, saying this was a fight for "global values."

"It is a global fight about global values -- it is about modernization, within Islam and outside of it," Blair said in a speech to the Los Angeles World Affairs Council.

"It is about whether our value system can be shown to be sufficiently robust, true, principle and appealing that it beats theirs," he said.

Blair called on people to reject religious extremism, saying extremism's whole strategy is based on a presumed sense of grievance that can motivate people to divide against each other.

"Our answer has to be a set of values strong enough to unite people with each other," he said.

Referring to the ongoing violence between Israel and Lebanon's Hezbollah, he said the conflict further showed that acts of terrorism were not isolated incidents.

"In the end, even the issue of Israel is just part of the same, wider struggle for the soul of the region," Blair said. "If we recognize this struggle for what it truly is, we would be at least along the first steps of the path to winning it. But I fear a vast part of the Western opinion is not remotely near this yet."

He accused Iran and Syria of supplying weapons to Hezbollah and financing militant elements of Hamas, urging the two countries to "come into the international community and play by the same rules as the rest of us, or be confronted."

"Their support of terrorism, their deliberate export of instability, their desire to see the democratic prospect wrecked in Iraq, is utterly unjustified, dangerous and wrong. If they keep raising the stakes, they will find they have miscalculated," he said.

Blair, who arrived here on Monday, was the first sitting British prime minister to visit Los Angeles.

On Monday, he and Californian Governor Arnold Schwarzenegger signed an agreement to cooperate in climate change and clean energy.