Gilani, who met US President George Bush in Washington on Monday, also said that his government was currently in the process of collecting more information about the incident.
The Bush administration has been tight-lipped about the attack by a Predator unmanned aerial drone inside Pakistan's northern areas bordering Afghanistan.
Both the Pentagon and the Central Intelligence Agency have kept mum about the incident and the State Department along with the White House have flatly refused to comment on 'reports'.
Bush appeared to have gone out of his way at his White House media briefing by mentioning the word "sovereignty", suggesting that Washington is mindful of this when it acts along the Pakistan-Afghanistan border.
But it is a well-known fact that American drones armed with Hellfire missiles routinely go after targets inside Pakistan in search of top al Qaeda and Taliban functionaries.
"..Because I'm here, I wanted to collect more details, but I have already talked to President Bush that there should be more cooperation on intelligence side, so that when there is a credible and actionable information given to us, we will hit ourselves," Gilani told CNN making the point that if the US goes about on its own it has more to lose than just trust.
"Basically,the Americans are a little impatient. Therefore, in future, I think we'll have more cooperation on intelligence side and we'll do the job ourselves" Gilani added.
Asked if the latest attack is a violation of Pakistani sovereignty, Gilani said: "Certainly, yes, if it is proved like this, it is certainly, yes."
But at the same time, Gilani said: "We have bilateral relations with United States on most of the areas, in defence, in science and technology, in education, in health, in food and agriculture, and of course we want to have more cooperation on the intelligence side."
Gilani said he had told Bush at their meeting that unilateral attacks against militants inside Pakistan should not be done."
"We must have more cooperation with each other and it's our job because we are fighting the war for ourselves," Gilani said.
The Pakistani leader is on a four-day visit to the United States .
