The Pakistani government has turned down Washington's invitation to jointly investigate a cross-border attack by NATO forces that killed 24 Pakistani soldiers, the U.S. Defense Department said Friday.

In a press briefing, Pentagon spokesman George Little said the Pakistani side has been invited to join the investigation and the U.S. side believes "their participation would be important as we look into this tragic incident."

However, Little said, Islamabad has "elected, to date, not to participate, but we would welcome their participation."

He said the relationship with Pakistan "remains very important to the United States," adding that the U.S. side believes that cooperation with Pakistan on a variety of fronts is essential.

"We realize the bumps in the road that we've experienced over the past several months," Little said. "We're going to work very hard to work with our Pakistani counterparts to get over this latest bump in the road."

The investigation, led by the U.S. Central Command, is likely to "look at the full range of factors that contributed to this tragedy and it will be broad, expansive and thorough."

On Nov. 26, a total of 24 Pakistani soldiers were killed and 13 others injured when NATO fighter jets and helicopters bombed two border posts in the Mohmand tribal region near the Afghan border.

The incident prompted angry protests from Islamabad. U.S. Secretary of State Hillary Clinton and Defense Secretary Leon Panetta issued a joint statement over the weekend to offer condolences, saying they are closely monitoring reports of the incident.

White House spokesman Jay Carney said Monday that the Obama administration took this matter "very seriously," vowing that the U.S. side will investigate the matter and is "very keen" on finding out what exactly happened.