The United States is working with Pakistan to make sure it has access to any information provided by the three widows of Usama bin Laden, a State Department spokesman said Tuesday, emphasizing cooperation between the two countries whose relationship has been badly hammered by the discovery and killing of bin Laden in Pakistan.

Spokesman Mark Toner said the U.S. is in discussions with the Pakistani authorities about a variety of sources of information relating to bin Laden's house and the people in it.

The United States is interested in making "sure we have access to any information that could contribute to our common goal here, which is continuing our counterterrorism cooperation and making progress against extremists in Pakistan and elsewhere."

Toner added that the U.S. is "optimistic that we'll be able to work through any obstacles and increase our information sharing."

Speaking on a plane to Texas, where President Obama was discussing immigration Tuesday, White House spokesman Jay Carney was less emphatic, saying that the relationship with Pakistan is "important and complicated."

However, Carney said he, too, was "optimistic" that counterterrorism cooperation with Pakistan will continue, particularly as the U.S. seeks access to bin Laden's wives "and also to the materials that were collected by the Pakistanis after the U.S. commandos left."

The three women and several of bin Laden's children have been in Pakistani custody since the May 1 raid by U.S. Navy SEALs on a massive compound in Abbottabad, Pakistan, where bin Laden was living.

The Al Qaeda leader was shot and killed in the raid, while his 29-year-old Yemeni wife, Amal Ahmed Abdulfattah, the youngest and apparent favorite of bin Laden, was wounded.

U.S. officials have identified the other two wives as Khairiah Sabar, also known as "Umm Hamza," and Siham Sabar, or "Umm Khalid.."

The expectation is that the three women will be repatriated to their home countries of Yemen and Saudi Arabia. However, earlier in the day, Pakistan foreign ministry spokeswoman Tehmina Janjua was quoted by AFP saying that the agency had not received extradition requests from the countries of origin for bin Laden's three wives.

A U.S. official rejected earlier assertions by Pakistani officials that the U.S. had not requested access to the women. Those claims "are simply not true," the official said.

The wives apparently have a lot of information to impart since they can explain how the compound functioned, who visited the compound, who facilitated the terrorist leader and bin Laden's state of mind.

"We know that you've been with him for a period of time. There's been these activities. And what type? How was the day spent?" Michael Balboni, a former homeland security adviser to Obama, suggested as questions to ask the women. "The littlest piece of information can help fill in the blanks that may be ... help put it into context as to how operational was Usama bin Laden and what type of communications was he actually able to make?"

Balboni and Michael Locker, managing director of the Investigative Project on Terrorism, said finding out who bin Laden met or spoke with is key because it will help pinpoint information about other operatives.

"You have a team of analysts combing over every piece of it to see what they have, what kind of patterns they can find. Maybe they have 100 documents that mention the same names or a pattern of phone numbers or addresses," Locker said.

Access to the women is one of many layers of tension between the two governments, which now also includes a denial by former Pakistani President Pervez Musharraf that his country had a deal to allow the United States to go after bin Laden within Pakistan's borders.

Many in the United States, including Obama, have also publicly questioned who was behind the support system that allowed bin Laden to live so close to Pakistani military for years.

Lt. Col. Tony Shaffer, a U.S. Army reservist who is at the Center for Advanced Defense Studies, said he thought it would be "virtually impossible" for the Pakistanis to deny the U.S. access to bin Laden's youngest wife.

"However, the Pakistanis and their response forward will be indicative of how much they're really on our side," he said, noting that "there's some embarrassing tidbits here that may come out potentially if we have direct access."

"And I think that's what's going to be the most telling aspect of whatever interrogation happens. ... So far, the Pakistani people and government in general have been very defensive about this whole situation," Shaffer said.

Fox News' Catherine Herridge and Craig Boswell contributed to this report.