Saudi Arabia's Crown Prince Mohammad bin Salman presents himself as a progressive leader and a supporter of women. But he's battling critics over the imprisonment of women, including Loujain al-Hathloul, a prominent advocate for women's rights — specifically, the right to drive.

The crown prince addressed her imprisonment in an interview with Norah O'Donnell for "60 Minutes."

"You understand the criticism, why give women the freedom to drive, and then imprison one of the most high-profile women who fought for the right to drive?" O'Donnell asked.

"The issue has nothing to do with that. As I mentioned to you in the beginning, there are laws in Saudi Arabia that must be respected, whether or not we agree with them, whether I personally agree with them or not," bin Salman said through a translator.

Women have seen their rights increase during the crown prince's rise to power. It's something he said he was working on when O'Donnell interviewed him last year.

The crown prince has given women the right to drive, he's relaxed the guardianship rules in which women needed permission from a male relative to key decisions about their lives; he's even said there's no religious requirement to cover one's head or one's face. But many of the women CBS News saw in Saudi Arabia still do that. They cover their faces and their heads and it was difficult to find any of them to talk to on camera.

Eventually, one woman agreed to speak.

"How would you describe how things are changing for women?" O'Donnell asked.

"It's amazing, it's totally different. Because a couple of years ago we couldn't walk like this freely," the woman said. "Life was different. People are accepting now that things are more open and free, it's different, it's really different."

During his interview with O'Donnell, the crown prince also denied being behind the brutal murder of Washington Post columnist Jamal Khashoggi. Although, he said he takes "full responsibility."

"When a crime is committed against a Saudi citizen by officials, working for the Saudi government, as a leader I must take responsibility. This was a mistake. And I must take all actions to avoid such a thing in the future," he said through a translator.