President Obama said Raymond Davis, left, enjoys diplomatic immunity under the Vienna Conventions [EPA]

An influential US senator has said his country is "deeply sorry" over the killing of two Pakistanis by a US official.

John Kerry, who is chairman of the Senate Foreign Relations Committee, delivered the apology after arriving in Pakistan on Tuesday to resolve a diplomatic row over the official named Raymond Davis.

"We are deeply, deeply sorry for that tragic incident," Kerry said soon after arriving in Pakistan's eastern city of Lahore.

"I want to come here to express our deepest regret for those tragic events and to express the sorrow of American people for the loss of life that has taken place."

Earlier, Barack Obama, speaking in Washington DC, urged Pakistan to free Davis while insisting that he was not "callous" about the shooting that led to the US employee's arrest.

In his first public remarks on a case that has cast a chill over an already strained partnership, the US president said Davis enjoyed diplomatic immunity under the Vienna Conventions.

"We expect Pakistan ... to abide by the same convention," Obama said.

"We're going to be continuing to work with the Pakistani government to get this person released.

"Obviously, we're concerned about the loss of life. We're not callous about that, but there is a broader principle at stake."

Diplomatic immunity

Davis insists he acted in self-defence when he shot dead two Pakistanis in the eastern city of Lahore on January 27.

Another Pakistani died when struck by a US diplomatic vehicle that came to Davis's assistance.

But many Pakistanis have been suspicious about Davis, who was arrested with loaded weapons and a GPS satellite tracking device. US authorities have been vague as to his role in Pakistan.

Obama said that diplomatic immunity was critical because otherwise diplomats who "deliver tough messages to countries where we disagree with them" will "start being vulnerable to prosecution locally".

"That's untenable. It means they can't do their job," Obama said.

The US has heaped pressure on Pakistan's weak government to free Davis, triggering a new flare-up in anti-US sentiment in the South Asian nation.

The US has put off three-way talks with Pakistan and Afghanistan that were due to be held next week.