(CNN) -- A Pakistani court has ordered a jailed American diplomat to remain in custody for 14 more days, authorities said Friday. The man's lawyer then filed a petition calling for his immediate release, saying he is covered under diplomatic immunity.
Raymond Davis, who allegedly shot and killed two men, was transferred from police custody to "judicial remand," said Munir Ahmed Khan, a member of the police investigative team.
Pakistani law says police can only keep a suspect in custody for 14 days. After that, a judge can either release the suspect -- on bail or for lack of evidence -- or transfer him to judicial custody, which is usually a prison instead of a police station lock-up.
Davis said he was attacked by the two men on January 27 who tried to rob him as he drove through a busy Lahore neighborhood, according to the U.S. Embassy in Pakistan.
The U.S. State Department has demanded that Davis be freed.
Under international agreements, people carrying diplomatic passports are granted diplomatic immunity, the department said.
Davis' lawyer filed a petition Friday, challenging the court's jurisdiction over the case. A judge will hear arguments on February 25.
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 rejected Davis' claim that he shot the men in self-defense.
"It was clear cut murder," Tareen told reporters.
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.
The detention has strained relations between the United States and Pakistan.
Secretary of State Hillary Clinton, according to the State Department, has raised the issue with Pakistani officials. And the U.S. ambassador to Pakistan, Cameron Munter, has met with Pakistani President Asif Ali Zardari on the issue.
Members of Congress told senior Pakistani leaders that billions of dollars of U.S. aid are in jeopardy unless Davis is released.
"We indicated it could very well be" that the United States might consider withholding funding, Rep. Howard "Buck" McKeon, R-California, said Tuesday after returning to Washington from meetings in Pakistan and Afghanistan.
McKeon said he and two other congressmen on the trip had frank conversations with Pakistani Prime Minister Yousaf Raza Gillani and other senior officials about Davis.
"It is entirely possible that a member of Congress would come down and offer an amendment to cut funding for Pakistan, based on their detaining Mr. Davis, and my guess is there would be a lot support for such an amendment, frankly because of the outrage of detaining an American with diplomatic immunity," said Rep. John Klein, R-Minnesota.
The U.S. spent more than $1.5 billion in non-military aid to Pakistan in fiscal year 2010.
The case has sparked some protest and fueled anti-American feelings in Pakistan.
During several protests last week, hard-line clerics condemned the shootings and demanded the government not release Davis to the U.S. government.
Local television showed a rally in Karachi where protesters re-enacted their version of the shooting. Men wearing smiling masks and holding toy guns played the part of Davis and gleefully danced around several protesters, who pretended to be the shooting victims.