Pre-trained transformer-based models have significantly advanced automatic speech recognition (ASR), yet they remain sensitive to accent and dialectal variations, resulting in elevated word error rates (WER) in linguistically diverse languages such as English and Persian. To address this challenge, we propose an accent-invariant ASR framework that integrates accent and dialect classification into the recognition pipeline. Our approach involves training a spectrogram-based classifier to capture accent-specific cues, masking the regions most influential to its predictions, and using the masked spectrograms for data augmentation. This enhances the robustness of ASR models against accent variability. We evaluate the method using both English and Persian speech. For Persian, we introduce a newly collected dataset spanning multiple regional accents, establishing the first systematic benchmark for accent variation in Persian ASR that fills a critical gap in multilingual speech research and provides a foundation for future studies on low-resource, linguistically diverse languages. Experimental results with the Whisper model demonstrate that our masking and augmentation strategy yields substantial WER reductions in both English and Persian settings, confirming the effectiveness of the approach. This research advances the development of multilingual ASR systems that are resilient to accent and dialect diversity. Code and dataset are publicly available at: https://github.com/MH-Sameti/Accent_invariant_ASR