At the same time, the Obama Administration maintained that it expects the Pakistan Government to continue to cooperate with the US in the ''war against terror''.
"We do not apologise for the action," White House Press Secretary Jay Carney told reporters at his daily news conference.
Carney was asked about the allegations by Gilani that the United States has violated Pakistan's sovereignty last week when its helicopters and special operation forces carried out a covert operation some 60 kilometers of Islamabad that kill Osama bin Laden.
"This relationship is too important to walk away from," Carney said when asked about the strain in the relationship between the two countries.
"The relationship is important and complicated. It has been cooperative in the past and we hope that it will continue to do so," he said.
Carney said that Obama Administration is in consultations with the Government of Pakistan at various levels on a host of issues including access to the three wives of Osama bin Laden, detained by Pakistani authorities from the Abbottabad hideout, and materials seized from there.
Acknowledging that there are differences between the two countries on a host of issues, the White House spokesman hoped that Pakistan would carry out a complete investigation as to how bin Laden was successful in staying in Abbottabad for so long.
The United States hopes that they will carry on the investigation as this is in the interest of both countries.
"The United States and Pakistan have an important, complicated relationship, as we've said. The cooperation that we've had with Pakistan has been important for years now in our fight against terrorism and terrorists. And more terrorists have been killed on Pakistani soil because of that cooperation than anywhere else in the world, and that's important to note," Carney said.