WASHINGTON (AFP) – Amid tensions between the United States and Pakistan over the killing of Osama bin Laden, a top US senator said Tuesday he will visit Islamabad seeking to mend ties and answer troubling questions.

US Senator John Kerry said he hoped to resolve some of the puzzles raised after the Al-Qaeda leader, the world's most wanted man, was finally tracked down to a Pakistani compound after a decade-long global hunt.

"There are some serious questions, obviously, there are some serious issues that we've just got to find a way to resolve together," he told reporters, adding that he would raise "all relevant issues" surrounding the May 2 raid.

Bin Laden, the architect of the September 11, 2001 attacks on the United States in which almost 3,000 people died, was killed in the raid by US forces on a compound in Abbottabad, just 55 kilometers (35 miles) from Islamabad.

There have been mounting allegations that he evaded capture for years thanks to either complicity or incompetence of Pakistani officials, since his compound was not far from a military academy and near the homes of retired generals.

Kerry, who chairs the Senate Foreign Relations Committee, said he would travel to Pakistan early next week "to get a dialogue going about the aftermath, and how we get on the right track."

Pakistan is a key, but uneasy, ally in the US-led war against the Taliban and Al-Qaeda insurgency in neighboring Afghanistan, and receives billions of dollars in US aid annually.

On Monday, Pakistan's Prime Minister Yousuf Raza Gilani dismissed as "absurd" accusations that Pakistani officials had helped bin Laden hide for years in the sizable compound, just two hours' drive from Islamabad.

He vowed a full investigation into the security and intelligence lapses.

With the pivotal US-Pakistan ties under severe strain, the White House has called on Islamabad to help counter the growing mistrust by granting American investigators access to three of bin Laden's wives detained after the raid.

The United States is keen to question the women in hopes of finding out more details of Al-Qaeda's reach and organization, as well as details of bin Laden's final years.

The US administration, which is also sifting through a trove of information and intelligence seized from bin Laden's compound, insisted Tuesday it was making "progress" in obtaining more information from Pakistan.

Pakistan said it had received no formal request for access to the women. A Pakistani official merely said: "The family's under treatment, they are under protective custody."

But earlier Tuesday, another US senator urged Pakistan to heed US "concerns" about its efforts to combat extremists, and give American interrogators access to the women.

"I think it's important that we have a good relationship with Pakistan, but not at any price," warned Senate Armed Services Committee Chairman Carl Levin.

Kerry, who traveled to Pakistan in February amid strained ties over a US contractor accused of shooting dead two Pakistanis in Lahore, has been a steadfast champion of greater US engagement in Pakistan.

The contractor, Raymond Davis, was eventually freed a few weeks later after $2 million in blood money was paid to the families of the dead.

Kerry's visit would be the highest profile stop in Pakistan since bin Laden's death, and could presage a trip to Islamabad by US Secretary of State Hillary Clinton.

Obama committed in late 2010 to travel to Pakistan this year, but the tensions in the wake of the bin Laden raid have cast further doubt on such a visit, and no trip has yet been put on his schedule.

Meanwhile, the sons of Osama bin Laden broke their silence Tuesday denouncing his "arbitrary killing" and burial at sea as the United States sought to question the Al-Qaeda leader's widows.

In a statement given to the New York Times, the sons asked why their father "was not arrested and tried in a court of law so that the truth is revealed to the people of the world."

"We maintain that arbitrary killing is not a solution to political problems," it said. In a separate statement posted on jihadist sites, the sons also slammed the "criminal mission" ordered by Obama which "obliterated an entire defenseless family."

The statements denouncing his father's killing are said to have been prepared at the direction of Omar bin Laden, 30, and also called for Pakistani authorities to release the Al-Qaeda leader's three wives and children.

Bin Laden's Yemeni wife, who was shot in the leg, has told Pakistani investigators that they lived in the Abbottabad compound for five years.

Omar bin Laden called for the family members to be released, and in the shorter statement released on jihadist websites said the family had been demeaned and humiliated by his father's burial at sea.

"It is unacceptable -- humanely and religiously -- to dispose of a person with such importance and status among his people, by throwing his body into the sea in that way," the statement translated by the SITE monitoring group said.

The New York Times meanwhile reported that the elite US Navy SEALs who gunned down bin Laden had permission to kill Pakistani forces if necessary during the operation.

"Their instructions were to avoid any confrontation if at all possible. But if they had to return fire to get out, they were authorized to do it," a senior administration official said.