Washington (CNN) -- U.S. President Barack Obama on Tuesday urged Pakistan to release a jailed U.S. diplomat accused of killing two people, warning that his prosecution could endanger the "important principle" of diplomatic immunity.
"Obviously, we're concerned about the loss of life. You know, we're not callous about that," Obama told reporters during a White House news conference Tuesday. "But there's a broader principle at stake that I think we have to uphold."
The detained man, Raymond Davis, is suspected in the shooting deaths of two Pakistani men in Lahore in January. He claimed he was defending himself against an attempted robbery, and the United States says he has diplomatic immunity.
His arrest has strained relations between the United States and Pakistan, a key ally in the war against al Qaeda and the Taliban in neighboring Afghanistan.
U.S. Sen. John Kerry, chairman of the Senate Foreign Relations Committee, arrived in Pakistan on Tuesday and expressed regret for the "extraordinarily unfortunate incident involving a diplomat assigned to the United States Embassy."
"I want to come here today to express our deepest regret for this tragic event and to express the sorrow of the American people for the loss of life that has taken place," Kerry told reporters in Lahore.
A government official told CNN that Kerry's trip to Lahore was at the administration's request "to help tone down the rhetoric and reaffirm our partnership with Pakistan."
While Kerry is not there to secure the diplomat's release, "certainly the Davis case will be a topic of discussion," said the official, who spoke about the trip on condition of anonymity because he was not authorized to speak publicly.
Kerry said the Davis case needs to be resolved so Washington and Islamabad can deal with bigger issues, like the struggle against Islamic militancy. While calling for the diplomat's release, he said the Justice Department "will conduct its own thorough criminal investigation regardless of immunity."
"We all live with the law of immunity, so we have to live within that context," Kerry said. He urged reporters to "help Pakistanis to see there are a lot of issues on the table that need to be handled in a fair way, and please help them understand this is not an American point of view."
Last week, a Pakistani court ordered Davis to remain in custody for 14 more days, and the lawyer for Davis then filed a petition calling for his immediate release on the grounds he is covered under diplomatic immunity.
A judge will hear arguments on the petition on February 25.
Davis, a contractor for the group Hyperion Protective Consultants LLC, was attached to the U.S. Embassy contingent in Pakistan as a "technical and administrative official," according to U.S. officials. Under international agreements, people carrying diplomatic passports are granted diplomatic immunity, the State Department says.
U.S. Secretary of State Hillary Clinton has raised the matter with Pakistani officials, and U.S. Congress members warn of a possible cut in nonmilitary aid to Pakistan, which was worth $1.5 billion in 2010, if Davis is not released.
The case has sparked protest and fueled anti-American feelings in Pakistan. During several protests earlier this month, hard-line clerics condemned the shootings and demanded the government not release Davis to the U.S. government.
Davis said he was attacked on January 27 by the two men, who tried to rob him as he drove through a busy Lahore neighborhood, according to the U.S. Embassy in Pakistan.
The United States says Davis was assigned to the U.S. Embassy in Islamabad but was working at the U.S. Consulate in Lahore at the time of the shootings.
Lahore Police Chief Aslam Tareen has rejected Davis' claim that he shot the men in self-defense, telling reporters, "It was clear-cut murder."
Witnesses told police that Davis kept firing even when one of the men was running away, Tareen said.
"It means he wanted to ensure that that they were killed," he said.
He acknowledged the two men shot were armed, and that one of them pointed his gun at Davis -- but didn't shoot.
"All the bullets were in their chamber," he said.
CNN correspondents Jill Dougherty and Reza Sayah contributed to this report.