Foreign Office spokesman Abdul Basit told a TV news channel today that the matter was already in court and the Punjab Police were investigating the shooting incident in Lahore on Thursday.
"It would not be appropriate to publicly talk on this issue," he said.
US Ambassador Cameron Munter raised the issue yesterday with former premier Nawaz Sharif, whose PML-N party rules Punjab.
Munter expressed regret over the death of Pakistani nationals in the Lahore incident and contended that the American should be handed over to US custody since he enjoyed diplomatic immunity.
Sharif "politely turned down the plea, saying that the matter was sub judice", the Dawn newspaper reported today.
PML-N spokesman Pervaiz Rashid told the media that Sharif believed the matter should be handled by the court.
The Foreign Office had rejected the US demand for freeing the American yesterday.
"This matter is sub-judice in a court of law and the legal process should be respected," spokesman Basit said in a statement.
The US had yesterday sought the immediate release of the American, identified in media reports as Raymond Davis, saying he was a diplomat and enjoyed diplomatic immunity.
The American shot and killed two armed youths who he claimed were trying to rob him.
A third Pakistani national died when he was hit by a US consulate car rushing to the aid of the American. The US embassy did an about-turn on the status of the American yesterday.
After initially describing him as a "staff member of the US Consulate General in Lahore", the US said yesterday he was a diplomat assigned to the embassy in Islamabad.
During a court appearance on Friday, the American said he had fired in self-defence. He is currently in police custody for six days.