Karzai had infuriated U.S. officials by accusing Washington of colluding with Taliban insurgents to keep Afghanistan weak even as the Obama administration presses ahead with plans to hand off security responsibility to Afghan forces and end NATO's combat mission by the end of next year.
But Kerry told a joint news conference that "I am confident (Karzai) does not believe the U.S. has any interest except to see the Taliban come to the table to make peace."
"So we're on the same page. I don't think there is any disagreement between us and I am comfortable with his explanation," Kerry said.
For his part, Karzai said "today was a very good day," citing the turnover of the detention facility at the U.S.-run Bagram military base north of Kabul.
The two spoke at a joint news conference during which Kerry also praised what he said was Afghanistan's commitment to "safe, secure" and transparent elections, scheduled for April 2014.
During Kerry's 24-hour visit to the country — his sixth since President Barack Obama became president but his first as Obama's secretary of State — Kerry also planned to meet with civic leaders and others to discuss continued U.S. assistance to the country and how to wean it from such aid as the international military operation winds down, and upcoming national elections.
U.S. officials accompanying Kerry said he did not plan to lecture Karzai on his earlier rhetoric, which the U.S. had seen as jeopardizing progress in the war against extremism.
Kerry, who arrived in Kabul from Amman, Jordan, had hoped also to travel to Pakistan on his trip to the region but put it off due to elections there. Instead, he met late Sunday in Amman with Pakistani army chief for Gen. Ashfaq Parvez Kayani, officials said.
The pair had a private dinner at the residence of the U.S. ambassador to Jordan as Pakistan continued to seethe in the aftermath of the return from exile to the country of former president Pervez Musharraf, himself a former army chief.
Earlier Monday, the U.S. military ceded control of the Parwan last detention facility near the U.S.-run Bagram military base north of Kabul, a year after the two sides initially agreed on the transfer. Karzai demanded control of Parwan as a matter of national sovereignty.
The top U.S. commander in Afghanistan, Gen. Joseph Dunford, handed over Parwan at a ceremony there after signing an agreement with Afghan Defense Minister Bismullah Khan Mohammadi. "This ceremony highlights an increasingly confident, capable and sovereign Afghanistan," Dunford said.
The dispute over the center threw a pall over the ongoing negotiations for a bilateral security agreement that would govern the presence of U.S. forces in Afghanistan after 2014.
An initial agreement to hand over Parwan was signed a year ago, but efforts to follow through on it constantly stumbled over American concerns that the Afghan government would release prisoners that it considered dangerous.
They have reason to worry. Zakir Qayyum — a former Guantanamo detainee, was released into Afghan custody in 2007. He was freed four months later and rejoined the Taliban. He has reportedly risen to become the No. 2 in the Taliban.
A key hurdle was a ruling by an Afghan judicial panel holding that administrative detention, the practice of holding someone without formal charges, violated the country's laws. The U.S. argued that international law allowed administrative detentions and also argued that it could not risk the passage of some high-value detainees to the notoriously corrupt Afghan court system.
An initial deadline for the full handover passed last September and another earlier this month.
The detention center houses about 3,000 prisoners and the majority are already under Afghan control. The United States had not handed over about 100, and some of those under American authority do not have the right to a trial because the U.S. considers them part of an ongoing conflict.
There are also about three dozen non-Afghan detainees, including Pakistanis and other nationals that will remain in American hands. The exact number and nationality of those detainees has never been made public.
A new agreement, or memorandum of understanding, was signed at the ceremony by Dunford and Khan, but the U.S. military said it will not be made public. The agreement supplants one signed last March, which had been made public.
The U.S. military said in a statement that the new agreement "affirms their mutual commitment to the lawful and humane treatment of detainees and their intention to protect the people of Afghanistan and coalition forces," an apparent reference to the release of detainees deemed to be dangerous.
There are about 100,000 coalition troops in Afghanistan, including about 66,000 from the United States. American officials have made no final decision on how many troops might remain in Afghanistan after 2014, although they have said as many as many as 12,000 U.S. and coalition forces could remain.
The U.S. started to hold detainees at Bagram Air Field in early 2002. For several years, prisoners were kept at a former Soviet aircraft machine plant converted into a lockup.
In 2009, the U.S. opened a new detention facility next door. The number of detainees incarcerated at that prison, renamed the Parwan Detention Facility, went from about 1,100 in September 2010 to more than 3,000.
After Monday's handover, it was renamed the Afghan National Detention Facility at Parwan and the U.S. military said it would provide the Afghan army with advisers and $39 million in funding.
The United States has spent about a quarter of a billion dollars to build the Bagram facility along with Kabul's main prison located in the capital.