The Winter War between Finland and the Soviet Union broke out on 30 November 1939. Like many of his fellow Flying Finns, including Gunnar Höckert and Lauri Lehtinen, Mäki was initially deployed on the Karelian Isthmus. However, along with Paavo Nurmi, he was sent on a tour of the United States in February 1940 in order to raise money for the Finnish Relief Fund. During the tour, which lasted for two months and culminated in an appearance in front of 14,000 people at Madison Square Garden, the two men raced against hand-picked American athletes. Mäki's times during the tour were well below those he had set the previous summer, the cause of which was a matter of much debate at the time. Mäki's career was cut short by service in World War II. The conflict had also caused the cancellation of the 1940 Summer Olympics in Helsinki, and with it ending Mäki's hopes of representing his country at the Olympic Games.