In the second day of an unannounced trip to Kabul, Kerry wants to advance negotiations that would allow U.S. forces to remain in Afghanistan after NATO forces leave in 2014, Voice of America reported.
Talks have been stalled on questions about Afghan sovereignty, the role of U.S. forces and a demand the U.S. will not again intervene in the country.
Negotiations have been under way for more than a year. Washington and Kabul hope to conclude an agreement by the end of this month, the report said.
The talks have been complicated by the seizure by U.S. forces a week ago of a senior Taliban official while he was in the custody of Afghan intelligence agents, The New York Times reported.
Latif Mehsud, a senior leader of the Pakistan Taliban, was on his way to Kabul to meet with Afghan intelligence officials when he was taken at gunpoint by U.S. forces. He had been a double agent for Afghanistan for the past two years.
The first day's talks were conducted after dinner Friday night, a senior State Department official said, when Kerry and Karzai took a short walk together alone. The conversation was described as being "candid about their differences," but with their points of contention being "narrowed."
A Karzai spokesman said the conversation had advanced negotiations over the security pact, Khaama Press reported.