The U.S. government on Thursday called for continued cooperation with Pakistan in the fight against al-Qaida, regarding it "essential" to its national security, as bilateral relations keep deteriorating this year.

"The relationship that we have with Pakistan is complicated, but very important," White House spokesman Jay Carney told reporters at a regular briefing.

Pakistan has been an important ally in the fight against al-Qaida, he said, pressing for continued cooperation with the Pakistanis on that front.

U.S.-Pakistani relations has been deteriorating since a secret U.S. commando mission killed al-Qaida leader Osama bin Laden in Pakistan in May without the knowledge from Islamabad.

The bilateral ties have been further damaged after Mike Mullen, chairman of U.S. Joint Chief of Staff, accused publicly last week the Haqqani network of being "a veritable arm" of Pakistan's intelligence service. Pakistan reacted furiously to Mullen's statement, warning that the U.S. might lose an ally of the war on terror.

"There's no question that we have disagreements, complications in our relationship, and we speak openly and candidly with our Pakistani counterparts about those," Carney said.

But the spokesman said the U.S. considers the relationship "important enough," and that the kind of cooperation America has with Pakistan is "essential" to its national security.

"We need to continue it precisely so we can most effectively take the fight to al-Qaida and succeed in that region," he said.

In the U.S. congress, it seems that pressure for more military actions in Pakistan beyond drone strikes is rising although the White House took a cautious approach on Wednesday, declining to endorse Mullen's remarks describing the Haqqani group as a virtual arm of Pakistan's Inter-Services Intelligence agency, for fear of losing Pakistan's help in the decade-long war in Afghanistan.