Hillary telephoned Gilani this evening and "conveyed her personal condolences on the deaths of Pakistani soldiers", said a statement issued by the Prime Minister's House.
Hillary said the "attack was not intentional" and asked Pakistan to "wait for the outcome of the investigation" into the incident.
In a bid to address concerns raised by Islamabad over what Pakistani military officials have described as an "unprovoked act of blatant aggression", Hillary said the US has the "highest regard for Pakistan's sovereignty".
She said: "This incident should not be allowed to jeopardise the bilateral relationship. Pakistan and US have common interests".
Hillary raised with Gilani the issue of Pakistan's participation in the Bonn Conference on Afghanistan to be held on December 5.
Gilani told her that the Parliamentary Committee on National Security had supported the cabinet's decision not to participate in the Bonn Conference.
Pakistan had played a positive role for peace and stability in the region and made many sacrifices in fighting terrorism, he said.
Pakistan's Parliament was "seized of the matter of terms of cooperation with the US", he told Hillary .
Gilani told Hillary that Pakistan had played a positive role for peace and stability in the region and made many sacrifices in fighting terrorism.
Pakistan's Parliament was "seized of the matter of terms of cooperation with the US," he said.
"This will ensure national ownership and clarity about the relationship," Gilani said.
Pakistan had responded angrily to the attack by NATO aircraft on two military border posts that killed 24 soldiers, including two officers, on November 26.
The government closed all NATO supply routes and asked the US to vacate Shamsi airbase, reportedly used by CIA-operated drones, by December 11.
Pakistan was expected to play a key role in the Bonn Conference, which is likely to discuss the future of Afghanistan and an endgame in the war-torn country.
On Friday, Gilani called for a comprehensive review of Pakistan's cooperation with the US and said troops had been instructed to respond "with full force" to any further act of aggression.
"Clearly, there is a limit to our patience. Cooperation cannot be a one-way street," he said.
The "dastardly" attack was a "grave infringement of Pakistan's territorial frontiers" by NATO and would "definitely compel us to revisit our national security paradigm", he told a key Parliamentary committee.
The Defence Committee of the Cabinet, the highest decision-making body on security issues, has already decided that the government will "undertake a complete review of all programmes, activities and cooperative arrangements" with the United States, NATO and ISAF, including "diplomatic, political, military and intelligence" cooperation.
US and Pakistani military officials have traded charges in recent days over the possible causes of the deadly air strike by the NATO aircraft.
Islamabad: A week after Pakistan-US ties plunged to a new low after a NATO attack that killed 24 Pakistani soldiers, Secretary of State Hillary Clinton on Sunday offered her personal condolences to Prime Minister Yousuf Raza Gilani but was unable to get Islamabad to reconsider its decision to boycott a crucial meeting on Afghanistan.
First Published: Sunday, December 04, 2011, 17:13