Lahore, Pakistan: US President Barack Obama said on Tuesday Pakistan must respect the diplomatic immunity of a US consular employee jailed for shooting dead two Pakistanis as Sen. John Kerry promised to subject the employee to a US criminal investigation if he is released by the Pakistani government.

Obama said Washington was working with Islamabad to secure the release of Raymond Davis, a former member of US special forces who said he acted in self defence in an armed robbery in the city of Lahore last month.

Washington says Davis has diplomatic immunity and should be released but the Pakistani government, fearful of a backlash from Pakistanis already wary of the United States and enraged by the shooting, says the matter should be decided in court.

"If our diplomats are in another country, then they are not subject to that country's local prosecution," Obama told a news conference in Washington.

"We respect it with respect to diplomats who are here."

Menwhile, Kerry expressed regret for the deaths of two Pakistani men in an apparent attempt to smooth over relations with the important ally in the war against extremists and al-Qaida while still insisting that the American needs to be released.

Kerry took a softer approach, saying that international law should not be abandoned, but also pledging that Davis would be fully investigated.

"It is customary in an incident like this for our government to conduct a criminal investigation. That is our law. And I can give you the full assurance of our government today that that will take place," Kerry told reporters on Tuesday in the eastern city of Lahore.

"So there is no such thing as a suggestion that something is out of law or that America thinks somehow we're not subject to the law."

Kerry spoke on a last-minute trip to Pakistan to try to heal relations over the case. He emphasised his sorrow over the incident and the deaths of the two men.

Freeing Davis could be risky for the unpopular Pakistani government, already struggling with a stagnant economy, growing discontent over rampant corruption, poverty and power cuts.

Pakistan's al Qaeda-linked Taliban warned earlier on Tuesday it would punish any move to release Davis.

"If (Pakistani) rulers hand him over to America then we will target these rulers. If Pakistani courts cannot punish Davis then they should hand him over to us," said its spokesman Azam Tariq.

"We will give exemplary punishment to the killer Davis."

The warning from the Taliban, which has kept up suicide bombings and remains a major security threat despite army offensives, adds to the charged atmosphere surrounding the case.

Cash-strapped Pakistan, one of the largest non-NATO recipients of American military aid, is loathe to risk losing US support by keeping Davis in jail but fears antagonising extremist groups who see the government as a US puppet.

The issue has become a lightning rod for anti-American sentiment in Pakistan, which the United States counts as an important, if unreliable, ally in its war against militancy.

A police report said Davis' assertions that he acted in self-defence were ‘apparently not correct’.

"The deceased Faizan Haider and Faheem Shamshad each received three bullets in the back of their bodies, which has also been corroborated by the post mortem report," it said.

A lawyer for Davis was not immediately available for comment.

Punjab province Law Minister Rana Sanaullah said the US embassy could ease public anger by issuing a statement saying Davis will face trial and ‘he will be given justice’.

Sanaullah said he did not see the benefit of a close relationship between Pakistan and the United States and blamed Washington for Pakistan's problems.

He warned that by demanding Davis' release the United States was giving clerics and religious parties the opportunity to ‘play with the emotions of the people’.