The offer of the investigation was conveyed by Senate Foreign Relations Committee Chairman John Kerry, who was dispatched to Pakistan by the Obama administration to calm tensions triggered by the arrest of US official Raymond Davis.
"Our department of justice will conduct its own thorough criminal investigation regardless of the immunity. We still believe the immunity applies but that doesn't mean we don't have the right under our law or the capacity to go through our own process," Kerry told a news conference shortly after he flew into Lahore.
He said it is customary for the US government to conduct a criminal investigation into incidents like the Lahore shooting. "That's our law. I can give you the full assurance of our government that it will take place," he added.
Kerry repeatedly expressed sorrow and regret on behalf of the US government and people for the incident in which Davis shot and killed two men.
Davis was arrested soon after the shooting in Lahore on January 27 and police have rejected his claim that he acted in self-defence as the two men were allegedly trying to rob him.
The incident took Pakistan-US relations to a new low over after senior Pakistani leaders rebuffed repeated American demands for Davis to be freed on the ground that he has diplomatic immunity.
Kerry stressed that the American demand for Davis' release was based not on "arrogance or special treatment" but on international law, including the Vienna Conventions that have been signed by both Pakistan and the US.
"Our department of justice will conduct a criminal investigation. That doesn't mean the law of immunity is something we don't have to respect," he said.
"It is the strong belief of our government that this case does not belong in the court and it does not belong in the court because this man has diplomatic immunity as an administrative and technical employee of the Embassy of the US in Islamabad," he added.
Asked about former Pakistani foreign minister Shah Mahmood Qureshi's reported remarks that the foreign office's records showed that Davis was not a diplomat entitled to immunity, Kerry noted that Qureshi's stance had been disputed by ruling Pakistan People's Party spokesperson Fauzia Wahab and Interior Minister Rehman Malik.
Malik, he said, had stated that he had documentation about Davis being a diplomat. Qureshi's people were contradicting him, he added.
Kerry stressed that Pakistan should not let this incident affect its relations with the US in a way that both countries could not address the "bigger issues" like strategic interests, stability in the region and the fight against radical extremists.
"We cannot allow one thing or another that might divide us in a small way to take away from the things that unite us in a big way," he said.
The senator, who is scheduled to meet Pakistani President Asif Ali Zardari and Prime Minister Yousuf Raza Gilani, said he would "listen" and work with the Pakistani leadership to find a way out of the impasse created by incident involving Davis.