On Saturday Sultan told state news station SPA: "When fathers, husbands and brothers ask us for women to drive we will look into it, though if they ask us the opposite we can't force them [to let women drive]."
Allowing women to drive has been a key demand of reformers in US-allied Saudi Arabia, which follows the austere Wahhabi school of Islam.
Religious scholars fear that driving would encourage women to mix with men outside their family. The ban is enforced in cities and on main roads but often flouted in rural areas.
King Abdullah, who this year ascended to the throne in the absolute monarchy, has said the promotion of women in society is a priority for Saudi Arabia's economic development, but any changes will be in line with Islamic principles.
Women were not allowed to run as candidates or vote in landmark elections for half the members of municipal councils held from February to April 2005. Officials have said they can take part in future polls.
But the Crown Prince suggested in his latest comments that the time was not right to hold elections to a key consultative assembly.
"We are not against elections but the public interest is for the people to join with its wise leaders in worldly and religious affairs"
The Crown Prince Sultan
Asked about the Shura council, which has the right to propose legislation, Sultan said: "We are not against elections but the public interest is for the people to join with its wise leaders in worldly and religious affairs.
"At any rate we already have the experience of the municipal elections, and those who wanted to take part managed to."
The Shura council has grown in influence in recent years.
Reformers want an elected parliament in Saudi Arabia, the birthplace of Islam.