Wolff, who in Friday practice with Williams at the British Grand Prix became the first woman in 22 years to take part in a Formula One weekend, made clear there were no hard feelings.
Interviewed by Spanish television, Perez had hailed Wolff as a great driver but than added jokingly that he would not want to be beaten by a female team mate and felt they would be better off in the kitchen.
The remarks flared up on social media and Perez subsequently put a message on Instagram apologising "with all my heart" to all women and Wolff in particular.
"It was never my intention to offend anyone," he said.
The Mexican also explained to his Twitter followers that "I never at any moment spoke badly of Susie. On the contrary, I have a very good relationship with her and admire her for being here."
Wolff, an experienced racer and the wife of Mercedes motorsport head Toto, defended the Force India driver - even if she could not resist a little dig in his direction.
"Saw some comments made by @SChecoPerez as I was making dinner in the kitchen last night...Please give him a break...," she Tweeted on Saturday.
"His comments were taken completely out of context. Anyway, as my family will tell you, I drive better than I cook!"
(Reporting by Alan Baldwin; Editing by John O'Brien)
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