Davis was arrested in Lahore on January 27 after he shot and killed two men he claimed were trying to rob him.
Police yesterday accused Davis of committing "cold-blooded murder" and said an investigation had produced no evidence of his claim of acting in self-defence.
"We understand that eyewitnesses at the scene said that (Davis) acted in self-defence when confronted with two armed men on a motorcycle. We also understand that these men were found with stolen property and, as the police stated today, a loaded gun," US Consul General Carmela Conroy said in a statement issued late last night.
"We regret that authorities did not consider these eyewitness accounts and physical evidence when they stated that this was not a case of self-defence," she said.
Davis was sent to prison yesterday after a court in Lahore remanded him to judicial custody for a fortnight.
But Conroy contended he should be "freed immediately" as he had diplomatic immunity.
"As a member of the Administrative and Technical staff at the US Embassy in Islamabad, Raymond Davis is entitled to full immunity from criminal prosecution by Pakistan under the Vienna Convention on Diplomatic Relations of 1961.
"All countries, including my country and your country, freely agreed to abide by these rules. Under the rules, he should be freed immediately," she said.
Conroy interacted with local and foreign journalists at her residence last night, the first time a US official has spoken in public with the media about the arrest of Davis.
Conroy also met Davis at the Kot Lakhpat jail, where he is being held.
The US respects "the law and Pakistan`s sovereignty" and the people of Pakistan and American officials "enjoy working and living in this country," Conroy said.
"Americans and Pakistanis can accomplish so much together. We need to resolve this case immediately and continue our work, including cooperation in education and health, our common fight against extremist violence, and building bridges between the people of Pakistan and America," she said.
"This incident was a tragedy, and we feel tremendous sorrow over the loss of life," she added.
The uneasy relations between the US and Pakistan have plunged to a new low over the case of Davis.
Pakistani leaders have rebuffed repeated US demands for the release of Davis, saying his case will be decided by the courts according to the country`s law.
Analysts believe the Pakistan government`s stance has been influenced by public anger over the episode and growing anti-American sentiments.
A third Pakistani was killed by a US consulate car rushing to help Davis and the widow of one of the men killed by Davis has committed suicide.