BOURNEMOUTH, England — Conservative lawmaker William Hague said Britain’s relationship with America needs to be “solid but never slavish,” a criticism of Prime Minister Blair’s outspoken support of American foreign policy.

“We need to know how we can manage an alliance with the U.S. that is not seen as one-sided,” Mr. Hague told the Conservative Party’s annual conference in Bournemouth, England.

The Conservatives are attempting to capitalize on discomfort among British voters about the deaths of British troops abroad and Mr. Blair’s support for President Bush. Mr. Hague, a former party leader who now handles foreign policy, must balance that effort against the traditional support of the Conservatives for America and pledges to keep forces in Iraq and Afghanistan.

“Blair is the first British prime minister to be called an American poodle,” Malcolm Rifkind, a former foreign secretary in John Major’s Conservative government, said in an interview Monday. “There’s a deep feeling the relationship shouldn’t be one of unconditional support.”

With 40 British soldiers killed this year in Afghanistan and 119 dead in Iraq since March 2003, British voters are increasingly concerned about Mr. Blair’s handling of those wars and Britain’s reputation abroad.

“The Atlantic alliance is the centerpiece of our security structure,” Liam Fox, the party’s lawmaker in charge of defense, said in an interview. “But Britain has to be a partner with the U.S., not a subordinate.”

Thirty-six percent of British voters supported the deployment in Iraq in July, down from 52% when America and Britain invaded in March 2003, according to a survey by ICM Ltd. About 51% of British voters now oppose the war, compared with 34% when fighting started.

Britain should be “avoiding the divisive rhetoric of a clash of civilizations,” Mr. Hague told the conference yesterday.

“Just as communism was defeated not only by arms but ideas, so our own moral authority is vital to the defeat of our newest enemies,” he said.

Mr. Blair’s refusal to criticize Israel’s bombing of Lebanon this summer depressed support for the Britain’s ruling Labour Party to 31%, according to surveys by YouGov Plc in August and September. That was the lowest rating for Labour since Mr. Blair took office in 1997.

“Normally, it’s the economy going wrong that brings governments down,” a professor of international relations at the London School of Economics, Mick Cox, said. “This time foreign policy is playing a very critical role.”

Still, the issues are difficult to exploit for the Conservatives. They backed Mr. Blair on taking troops into the Iraq war. And they say that if they were in government yesterday, they wouldn’t pull out either there or in Afghanistan.

“We have to succeed in Afghanistan,” Mr. Fox said. In Iraq, “we have to live with the mistakes and stay the course if we don’t want to create the conditions under which terrorism would flourish.”

Mr. Hague said Mr. Blair’s policies in the Middle East are impractical and unrealistic.

“We are skeptical of grandiose visions to remake the world,” Mr. Hague said in an interview ahead of his speech. “We will work on the basis of real understanding of the complexities of the Middle East and different nations around the world.”

While David Cameron has used his 10 months as leader to broaden the Conservative Party’s appeal by focusing on issues such as the environment and rejecting calls from within his party to push for tax cuts, he will have a harder time finding middle ground on foreign and defense issues.