Karzai's comments were made during a speech at a youth conference in Kabul, the Khaama Press reported.
Karzai said the deal should provide financial support to Afghanistan, provide for the security of the country and respect its sovereignty.
The deal between the United States and Afghanistan would provide a legal basis for foreign troops to stay in the country after 2014, the deadline for the withdrawal of NATO combat troops from the country.
Karzai's comments came a day after President Barack Obama's special representative for Afghanistan, James Dobbins, said he was optimistic a security deal could be signed in October, Khaama Press said.
Florida bear attack: Black bear mauls woman's face
Ron Burgundy interviews Peyton Manning on SportsCenter