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 earlier in the week 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 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, saying the phone calls were a public relations move by the ministry to help people understand that laws would be "fully enforced" Saturday.
'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 was 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 driving campaign is activist Manal Al-Sharif, who was jailed for more than a week in 2011 after posting a video of herself driving.
Al-Sharif, who now lives in the United Arab Emirates, said it is a positive sign that the government 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."
Saturday's protest was the culmination of an online movement launched in late September urging Saudi women to get behind the wheel.
The campaign quickly gained momentum, with its online petition garnering more than 16,000 signatures despite the kingdom's restrictions on protests.
The online initiative was 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 allow women to drive and not punish those campaigning for change.
The group said at least 35 women drove on Saudi streets Saturday, filming and uploading their videos on to YouTube.