(CNN) -- Women in Saudi Arabia demonstrated Saturday against their nation's de facto ban on women driving -- by getting behind the steering wheel.
The campaign for change has been gathering pace on social media, with numerous women filming themselves behind the wheel in various cities, and then uploading those videos to YouTube.
Several Saudi supporters of the campaign told CNN that at least 23 women had driven so far Saturday, and that more planned to do so.
No one has been arrested but an increased security presence has been reported on the capital's streets.
Driving campaign supporter Mai Al-Swayan, an economic researcher, told CNN she is one of the women who drove Saturday -- and posted a video of her action to YouTube.
She said she drove from home to a grocery store in Riyadh, and then back with her groceries. "I drove on the highway and was noticed by a couple of cars but they were fine with it," she said.
"I'm very proud. I feel like we accomplished the purpose of our campaign."
Al-Swayan, who has taken the wheel before in defiance of the ban, said she was worried about what might happen before she drove Saturday, but now plans to keep driving.
She believes more women will go out and drive on Saturday and in the days to come.
Interior Ministry: Laws will be enforced
Asked if any women had been observed or stopped from driving, or if there was an increased police presence on the streets of major cities, Saudi Arabia's Interior Ministry spokesman Mansour Al-Turki said, "It's a normal day, just like every Saturday."
He added, "I am not aware of any violation. Usually regional police spokesmen would speak to media about any, if any violation takes place."
Saudi Arabia's Interior Ministry issued a warning Wednesday to women caught driving and anyone taking part in demonstrations.
Without outlining how laws would be applied and what punishment might be doled out to offenders, Al-Turki said then, "All violations will be dealt with -- whether demonstrations or women driving."
He added, "Not just on the 26th. Before and after. At all times."
No traffic law specifically prohibits women from driving in Saudi Arabia, but religious edicts there are often interpreted to mean women are not allowed to operate a vehicle.
It's not clear what action might be taken against women who defy the de facto ban.
Several Saudi women supporting the October 26th Women's Driving Campaign said they received threatening calls Thursday from men claiming to represent the Interior Ministry, according to women's rights activists who requested anonymity. The callers warned the women not to drive before, on or after Saturday, the activists said.
Initially, Al-Turki denied any calls were made. He later contacted CNN to clarify his comments.
He said the phone calls were a public relations move the ministry undertook to help some people understand a statement made Wednesday, which said laws would be "fully enforced" Saturday. This will apply to female drivers and those who might stage protests in a nation where they're outlawed. Saudi Arabia has tight controls on all gatherings.
'Shameful' to detain women for driving
Adam Coogle, a Saudi Arabia researcher for Human Rights Watch, told CNN via e-mail that the Saudi Interior Ministry "is trying to deflate the momentum" behind the campaign through "direct, individual intimidation."
He called on Saudi Arabia to end discrimination and allow women to go about their business.
"It is shameful that a woman could be detained for activity that isn't illegal," he said. "The Interior Ministry claims it is against 'activities that disturb public peace,' but pulling over and arresting activists merely for practicing their rights is a far greater threat to public peace than merely getting behind the wheel."
One of those spearheading the campaign is activist Manal Al-Sharif, who lives in the United Arab Emirates after being jailed for a week after posting a video of herself driving in 2011.
She said she is taking it as a positive sign that the government has stated its position on women driving.
"They kept telling the world that the women's driving issue was one for Saudi society to decide upon," she said. "Society is now showing it is supportive of the idea of women driving. The government's reaction makes it very clear this is not a societal decision. This is a political decision."
'Discriminatory and demeaning to women'
Saturday's protest was the culmination of an online movement launched in late September urging Saudi women to get behind the wheel.
The October 26th Women's Driving Campaign quickly gained momentum, with its online petition garnering more than 16,000 signatures despite the kingdom's restrictions on protest.
The online initiative has been
boosted by the fact that residents of Saudi Arabia are highly active on social media and YouTube.
Rights group Amnesty International on Thursday urged Saudi Arabia to lift the ban on women driving -- and not to punish those campaigning for change.
"It is astonishing that in the 21st century the Saudi Arabian authorities continue to deny women the right to legally drive a car," said Philip Luther, director of the group's Middle East and North Africa program.
"The driving ban is inherently discriminatory and demeaning to women and must be overturned immediately. It is completely unacceptable for the authorities to stand in the way of activists planning to campaign against it."
According to Amnesty International, at least 35 women have already taken to the Saudi streets driving their cars, filming and uploading their videos on to YouTube.
Amnesty points out that the current situation makes Saudi women dependent on men to carry out simple daily tasks requiring transport, such as traveling to work or university, and taking their children to school.
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