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Andrew Tyrie, a British lawmaker who heads a group of legislators investigating so-called extraordinary rendition, said he hoped the British inquiry would get to “the truth about alleged British complicity in the kidnap and torture of detainees.”

Mr. Cameron confirmed that Mahmoud Jibril, the head of the Libyan rebels’ acting Cabinet, has assured Britain that the country’s post-Gadhafi regime would assist British police hunting the killer of a policewoman shot dead outside the Libyan Embassy in London in 1984.

Since the NATO-led air campaign began in Libya on March 19, British fighter jets have flown 2,400 sorties — about one fifth of the total, Mr. Cameron told the House of Commons. He said that the mission would not end until the threat from Gadhafi loyalists has been fully suppressed.

“Those thinking NATO will somehow pull out or pull back must think again. We are ready to extend the NATO mandate for as long as is necessary,” he said.

Britain and NATO partners also will assist Libya‘s interim government in bringing Col. Gadhafi to justice, Mr. Cameron said.

“This is a man whose crimes are becoming ever more apparent every day and who is wanted by the International Criminal Court. There must be no bolt-hole, no pampered hiding place from justice. He must face the consequences of his actions, under international and Libyan law,” he told legislators.

Mr. Cameron said Britain’s top diplomat in Libya and other officials would move from a current base in Benghazi to Tripoli to prepare to reopen the U.K. Embassy.

He also repeated calls for Syrian President Bashar Assad to stand down and to halt violence that the United Nations estimates has seen 2,200 people killed since a crackdown on protests began mid-March

“The achievement of the Libyan people gives hope to those across the wider region who want a job, a voice and a stake in how their society is run,” Mr. Cameron said. “The message to President Assad must be clear: He has lost all legitimacy and can no longer claim to lead Syria. The violence must end.”