Members of parliament told RFE/RL's Radio Free Afghanistan said the process could last two weeks.
Each minister proposed must win a separate vote of confidence. Other details have yet to be resolved. Some members of parliament, for example, want each nominee to present a specific plan to the Wolesi Jirga.
Other members of parliament say they do not want the result of any vote to be counted or announced until all of the nominations have been debated and voted on separately.
A third group of parliamentarians has asked that the votes of confidence be conducted by secret ballot. They cite concerns about personal safety if the votes are made public.
Karzai is attending today's parliamentary session, along with his first vice president, Hamad Zia Massoud, and the 25 proposed ministers.