Periodical daily variation in the number of reported COVID-19 cases within weeks is a common observation in global and national statistics. This variation may imply that the day of week has a significant role in the number of reported cases. We compared the pattern in some countries with an acceptable surveillance system. Data of 18 European and North American countries between 6 Mar and 8 Nov 2020 were extracts. Harmonic regression models were used to quantify the peak day, the absolute intensity and the average of coefficient of variation within weeks (ACVW) classified by country. In eight countries, the within week variation was statistically significant, the maximum and minimum number reported cases were in Saturday and Monday respectively, however, this pattern varied among countries. The maximum of ACVW was observed in Belgium and France, while it was minimum in Russia. The level of intensity of infection had a positive association with the ACVW (r = 0.54, p-value = 0.021). The observed variation and its pattern may show that the coverage or the tidiness of COVID-19 surveillance system fluctuates in different days of week. In addition, we suggest that the level of this fluctuation might be used as an accuracy indicator of the surveillance system.