ISI chief, Pasha told the in-camera joint session of the Senate and National Assembly on Friday that he had stressed the need to formalise the relationship through an agreement during a recent meeting with CIA head Leon Panetta.
"It is not possible to carry forward the cooperation without a formal agreement duly approved by parliament," Pasha was quoted as saying by an unnamed lawmaker who spoke to Dawn newspaper.
Several media accounts of the joint session have said that Pasha had described his meeting with Panetta as stormy.
One report quoted lawmakers as saying that Pasha had claimed he had a "shouting match" with Panetta during the recent meeting in the US.
Pasha said his agency had always cooperated with the CIA and the American spy agency`s successes in the war against terrorism were made possible because of vital information passed on to it by the ISI, the Dawn reported.
He denied the ISI had concealed anything from the CIA.
"In fact, it is the other way round," Pasha was quoted as saying.
Citing an example of the CIA`s "withholding" of information, Pasha said the ISI had provided information about Abu Ahmad Al-Kuwaiti, the courier who led the US to bin Laden.
When the CIA, acting on this lead, arrested one of Al-Kuwaiti`s friends in Kuwait, it did not share the development with the ISI, Pasha reportedly said.
Pasha said Pakistan would have taken appropriate measures to kill or arrest Taliban leaders who entered the country through the porous border with Afghanistan after the massive bombing of Tora Bora mountains had advance information been provided by the CIA.
Rejecting allegations that bin Laden was brought to the garrison city of Abbottabad by the ISI, Pasha said: "Why would the ISI keep him at a place without escape route and proper security cover?"
"The fear that we cannot live without America has taken away our self-respect. Are we to live in humiliation out of the US fear forever," Pasha was quoted as saying.
In an apparent response to statements from New Delhi that India too can carry out strikes inside Pakistan, Pasha said any attack from the east would invite a befitting response.
He said a contingency plan is in place and targets inside "India had already been identified".
Pasha told the lawmakers: "We have also carried out rehearsal for it."
Another report in The News daily quoted PML-N lawmaker Mushahidullah Khan as saying that Pasha told the joint session that CIA contractor Raymond Davis was handed over to the US on the orders of President Asif Ali Zardari and Prime Minister Yousuf Raza Gilani.
Khan said Pasha stated: "We advised the government to resolve the issue. But we did what we were finally asked by the President and the Prime Minister to do."
"Pasha initially tried to evade the questions but later said the ISI has acted on the advice of the Prime Minister and the President," another unnamed lawmaker told the newspaper.
Pasha did not reveal who paid blood money to the two men killed by Davis, where the deal was finalised and the whereabouts of the families of the two dead men.
Khan said he had stated during the joint session that the ISI should not make or break political parties or create favourites in any political force.
Pasha responded by reportedly sayings: "On our own, we have decided to stay away from politics; and when I meet the army chief, he too says there will be no derailing of the democratic system."