A polite expression meaning 'don't worry about it' or 'please don't concern yourself'; often used in formal situations to reassure someone.
遅れてしまい申し訳ありません。— いいえ、お気になさらず。
— I'm sorry I'm late. — No, don't worry about it.
プレゼントは気に入らなければお気になさらず、そのまま返してください。
If you don't like the gift, please don't worry about it and just return it.
ご心配いただきありがとうございます。どうぞお気になさらずにお過ごしください。
Thank you for your concern. Please, don't worry and carry on.