The number of new Covid-19 cases is still high in several countries, despite vaccination efforts. A number of countries are experiencing new and severe waves of infection. Therefore, the availability of reliable forecasts for the number of cases and deaths in the coming days is of fundamental importance. We propose a simple statistical method for short-term real-time forecasting of the number of Covid-19 cases and fatalities in countries that are latecomers—i.e., countries where cases of the disease started to appear some time after others. In particular, we propose a penalized LASSO regression model with an error correction mechanism to construct a model of a latecomer country in terms of other countries that were at a similar stage of the pandemic some days before. By tracking the number of cases in those countries, we use an adaptive rolling-window scheme to forecast the number of cases and deaths in the latecomer. We apply this methodology to 45 countries and we provide detailed results for four of them: Brazil, Chile, Mexico, and Portugal. We show that the methodology performs very well when compared to alternative methods. These forecasts aim to foster better short-run management of the healthcare system and can be applied not only to countries but also to different regions within a country. Finally, the modeling framework derived in the paper can be applied to other infectious diseases.