The deal is aimed at establishing the legal base for the continued presence of several thousand U.S. troops in Afghanistan after the 2014 withdrawal deadline, and also detail a U.S. commitment to continue aid and support to the Afghan government for the next 10 years.
Recent reports have suggested that negotiations have stalled over the issue of the transfer of U.S.-held detainees to Afghan control, as well as night raids on suspected militants by U.S.-led forces .
The reported snags in the talks come as U.S.-Afghan relations have been embittered by an incident last month in which copies of the Koran, the Islamic holy book, were burned at the NATO-run Bagram base near Kabul.
The February 20 burning -- which U.S. officials say was a mistake -- sparked six days of violent anti-American protests in which more than 30 people were killed, and led to an apology from U.S. President Barack Obama.
Karzai, in response to a question by RFE/RL's Radio Free Afghanistan at a news conference in Kabul on March 6, said "there has been progress" in talks with the United States, but that his government was seeking to increase it.
"Yes, Afghanistan has its own terms for the strategic relations with the U.S. and those terms were set by the loya jirga," or grand council, Karzai said.
"We are working on it with the U.S. government. During the last week there has been progress in this regard. We also had negotiations yesterday," he added. "We had some questions and asked for clarifications. There has been progress, but Afghanistan is seeking to increase it."
An Afghan government spokesman, Aimal Faizi, said Karzai met U.S. Ambassador Ryan Crocker and General John Allen, the NATO commander in Afghanistan, on March 5.
The spokesman said that in the meeting, the three men discussed a U.S. proposal to hand over the main prison in the country, a detention facility next to the Bagram base, to Afghan control within six months.
Karzai had initially demanded that the prison be handed over by early February, then extended the deadline to March 9.
The Afghan spokesman said the three men also discussed the issue of night raids. Karzai wants an immediate halt to the night raids -- but U.S. forces argue that such operations are critical to success in the fight against insurgents.
U.S. Embassy spokesman Gavin Sundwall declined to disclose any details about the March 5 meeting.