Background: Timely monitoring of COVID-19 impact on mortality is critical for rapid risk assessment and public health action. Aim: Building upon well-established models to estimate influenza-related mortality, we propose a new statistical Attributable Mortality Model (AttMOMO), which estimates mortality attributable to one or more pathogens simultaneously (e.g. SARS-CoV-2 and seasonal influenza viruses), while adjusting for seasonality and excess temperatures. Methods: Data from Nationwide Danish registers from 2014-week(W)W27 to 2020-W22 were used to exemplify utilities of the model, and to estimate COVID-19 and influenza attributable mortality from 2019-W40 to 2020-W20. Results: SARS-CoV-2 was registered in Denmark from 2020-W09. Mortality attributable to COVID-19 in Denmark increased steeply, and peaked in 2020-W14. As preventive measures and national lockdown were implemented from 2020-W12, the attributable mortality started declining within a few weeks. Mortality attributable to COVID-19 from 2020-W09 to 2020-W20 was estimated to 16.2 (95% confidence interval (CI): 12.0 to 20.4) per 100, 000 person-years. The 2019/20 influenza season was mild with few deaths attributable to influenza, 3.2 (95% CI: 1.1 to 5.4) per 100, 000 person-years. Conclusion: AttMOMO estimates mortality attributable to several pathogens simultaneously, providing a fuller picture of mortality by COVID-19 during the pandemic in the context of other seasonal diseases and mortality patterns. Using Danish data, we show that the model accurately estimates mortality attributable to COVID-19 and influenza, respectively. We propose using standardised indicators for pathogen circulation in the population, to make estimates comparable between countries and applicable for timely monitoring.