The discovery of the al Qaeda leader in a garrison town just 50 km (30 miles) away from the capital, Islamabad, on May 2 raised fresh doubts about Pakistan's reliability as a partner in the U.S.-led war on militancy.
"They have cooperated; we have always wanted more," a U.S. official told reporters traveling on Clinton's plane ahead of the surprise visit.
"They have actually, from their perspective, done a lot. What they have never really grasped is how much more they have to do in order to protect themselves and, from our point of view, protect our interests and assist us in ways that are going to facilitate our transition in Afghanistan."
The Pakistan government welcomed the death of bin Laden but was outraged and embarrassed by the secret Navy SEALs raid in the town of Abbottabad, where bin Laden had lived for years, as a breach of its sovereignty.
It was the latest in a series of incidents, from U.S. drone attacks inside Pakistan to the arrest of a CIA contractor for killing two Pakistanis that have strained ties.
There has also been scant evidence of Islamist militancy abating despite billions of dollars in U.S. aid.
Thursday, a suicide car bomber killed 27 people outside a police station in the northwestern town of Hangu, and last weekend a group of militants stormed a heavily guarded naval base in the city of Karachi and fought a 16-hour pitched battle with hundreds of soldiers.
These attacks have raised fresh doubts about Pakistan's ability to quell militancy and protect its nuclear arsenal.
Clinton and U.S. Joint Chiefs of Staff Admiral Mike Mullen were due to meet President Asif Ali Zardari as well as Army chief General Ashfaq Kayani and the head of the ISI spy agency, Lieutenant-General Ahmad Shuja Pasha.
CIA TEAM TO SCOUR BIN LADEN HIDEOUT
In the latest sign of deepening distrust between Washington and Islamabad, Pakistan has told the United States to halve the number of military trainers stationed in the country.
However, the U.S. official said Washington had seen some signs of improved Pakistani cooperation, including the return of the tail section of a helicopter that crashed during the night-time raid in Abbottabad and access to bin Laden's wives.
In a further apparent move to reduce tensions, Pakistani authorities have agreed to allow the CIA to send a forensic team to scour the former hide-out of bin Laden for new clues.
A U.S. official in Washington, who asked for anonymity while discussing sensitive information, said the forensic experts would look for evidence hidden in walls or buried under floors, but there was no guarantee they would find anything.
Many U.S. lawmakers, skeptical that Pakistani officials did not know of bin Laden's presence, want to cut U.S. aid to Pakistan, which the White House views as vital to counter-terrorism and to hopes of stabilizing neighboring Afghanistan.
Just a day before coming to Pakistan, Clinton said working with Pakistan was a strategic necessity for the United States, even as she pressed Islamabad to act more decisively to counter terrorism.
She praised Pakistan as a "good partner" in global efforts to fight terrorism, though she acknowledged that the two countries have disagreed on how hard to fight al Qaeda, Afghan Taliban fighters and other militants.
"We do have a set of expectations that we are looking for the Pakistani government to meet but I want to underscore, in conclusion, that it is not as though they have been on the sidelines," she told a news conference in Paris Thursday.
"They have been actively engaged in their own bitter fight with these terrorist extremists."