Caroline Wozniacki was pleased with her battling display at the Madrid Open on Monday as she kept her quest to become world number one on track with a hard-fought victory over Ashleigh Barty.

Wozniacki will usurp Simona Halep at the top of the rankings if she is victorious in Madrid this week, but her progression into round three was far from easy.

Clay is far from the Dane's favourite surface so she was delighted to come back from 4-2 down in the deciding set to win 6-2 4-6 6-4.

"I think there's a lot of positives to take with me. I thought we played pretty well," she told a media conference.

"The first set I won 6-2, but I made most of my shots. I got the important ones, as well. Even when I was down love-40, I still managed to come back.

"In the second set, the only negative I can say I think I didn't play my best game when I was up 4-3 and serving. I made a double-fault. She also played a really good game, so... I wish I could have just gotten it right then and there.

"I think there's a lot of positives to take with me. I thought she played really well. I think I played well, served well. I moved pretty well. I have to say I think there's a lot of big things coming from her. I think we will see a lot of her in the future, as well."

Second seed Wozniacki will meet Kiki Bertens in round three, another opponent the Australian Open champion is wary of.

"It'll be another tough match," she added. "She's a big server with a big forehand. She loves the clay. 

"I haven't had an easy draw here, but I don't think anyone has. It's just about going for it again. That's all I can do, is go out there and do my best.

"I think it's definitely a surface that I think evens out a lot of the playing field. I think there's more people that have an opportunity here on this surface.

"I played a final on clay last year. I think I played Stuttgart finals a few years back. There was one year I didn't play on clay at all. It's just I think part of the progress.

"I actually don't mind it. It's not my favourite surface, but I think I can play well on it. It's just all about getting the mental attitude right. I think I have that. Then you just kind of take it from there."