Deaths are frequently under-estimated during emergencies, times when accurate mortality estimates are crucial for emergency response. This study estimates excess all-cause, pneumonia and influenza mortality during the coronavirus disease 2019 (COVID-19) pandemic using the 11 September 2020 release of weekly mortality data from the United States (U.S.) Mortality Surveillance System (MSS) from 27 September 2015 to 9 May 2020, using semiparametric and conventional time-series models in 13 states with high reported COVID-19 deaths and apparently complete mortality data: California, Colorado, Connecticut, Florida, Illinois, Indiana, Louisiana, Massachusetts, Michigan, New Jersey, New York, Pennsylvania and Washington. We estimated greater excess mortality than official COVID-19 mortality in the U.S. (excess mortality 95% confidence interval (CI) 100 013–127 501 vs. 78 834 COVID-19 deaths) and 9 states: California (excess mortality 95% CI 3338–6344) vs. 2849 COVID-19 deaths); Connecticut (excess mortality 95% CI 3095–3952) vs. 2932 COVID-19 deaths); Illinois (95% CI 4646–6111) vs. 3525 COVID-19 deaths); Louisiana (excess mortality 95% CI 2341–3183 vs. 2267 COVID-19 deaths); Massachusetts (95% CI 5562–7201 vs. 5050 COVID-19 deaths); New Jersey (95% CI 13 170–16 058 vs. 10 465 COVID-19 deaths); New York (95% CI 32 538–39 960 vs. 26 584 COVID-19 deaths); and Pennsylvania (95% CI 5125–6560 vs. 3793 COVID-19 deaths). Conventional model results were consistent with semiparametric results but less precise. Significant excess pneumonia deaths were also found for all locations and we estimated hundreds of excess influenza deaths in New York. We find that official COVID-19 mortality substantially understates actual mortality, excess deaths cannot be explained entirely by official COVID-19 death counts. Mortality reporting lags appeared to worsen during the pandemic, when timeliness in surveillance systems was most crucial for improving pandemic response.