Under Saudi law, a woman must have permission from a male family member, normally the father, husband or brother - in the case of a widow, sometimes her son - to obtain a passport, marry, travel, exit prison and sometimes work or access health care.
In recent years, the Al Saud regime has come under intense pressure by rights groups for mistreating women.
Reports said on Tuesday that some 14,700 people have signed the petition - the first of its kind in the kingdom.
Campaigner Aziza al-Yousef of Riyadh told AFP that the online petition calls for Saudi women to be treated "as a full citizen, and decide an age where she will be an adult and will be responsible for her own acts.”
Yousef further noted that she took the petition to the Royal Court in person on Monday, but was advised to send it by mail.
Nassima al-Sadah, an activist in Eastern Province, also expressed her dissatisfaction with the contentious system, saying, “We are suffering from this guardianship system.”
Back in July, Human Rights Watch (HRW) published a blistering report on the issue of women’s rights in Saudi Arabia, which found that female citizens were treated as inferior to men.
"Saudi Arabia's male guardianship system remains the most significant impediment to women's rights in the country despite limited reforms over the last decade," the rights organization said.
In response to the HRW report, Saudi women began tweeting using the hashtag #StopEnslavingSaudiWomen.
HRW researcher, Kristine Beckerle, who worked on the report, described the response as "incredible and unprecedented.”
Saudi women have “made undeniably clear they won't stand to be treated as second-class citizens any longer, and it's high time their government listened,” she added.
Saudi Arabia is the only country in the world that prohibits women from driving. The ban stems from a religious fatwa imposed by Wahhabi clerics. If women get behind the wheel in the kingdom, they may be arrested, sent to court and even flogged.
In 2012, the then Saudi King, Abdullah bin Abdulaziz Al Saud, announced that women would be given the right to vote and run in municipal elections for the first time in the country. He also appointed 30 women to the country’s top advisory Shura Council before his death in January 2015.
Last December, Saudi women voted and stood as candidates for the first time in the country's municipal elections.
Approximately 10 million women and girls are living in Saudi Arabia, Press TV reported.
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