Background: After the outbreak of the corona virus disease-19 (COVID-19) pandemic, teledermatology was implemented in the Hungarian public healthcare system for the first time. Our objective was to assess aggregated diagnostic agreements and to determine the effectiveness of an asynchronous teledermatology system for skin cancer screening. Methods: This retrospective single-center study included cases submitted for teledermatology consultation during the first wave of the COVID-19 pandemic. Follow-up of the patients was performed to collect the results of any subsequent personal examination. Results: 749 patients with 779 lesions were involved. 15 malignant melanomas (9.9%), 78 basal cell carcinomas (51.3%), 21 squamous cell carcinomas (13.8%), 7 other malignancies (4.6%) and 31 actinic keratoses (20.4%) were confirmed. 87 malignancies were diagnosed in the high-urgency group (42.2%), 49 malignancies in the moderate-urgency group (21.6%) and 16 malignancies in the low-urgency group (4.6%) (p < 0.0001). Agreement of malignancies was substantial for primary (86.3%; κ = 0.647) and aggregated diagnoses (85.3%; κ = 0.644). Agreement of total lesions was also substantial for primary (81.2%; κ = 0.769) and aggregated diagnoses (87.9%; κ = 0.754). Conclusions: Our findings showed that asynchronous teledermatology using a mobile phone application served as an accurate skin cancer screening system during the first wave of the COVID-19 pandemic.