Final answer:
Stalin supported Kim Il-sung's invasion of South Korea based on the belief that the US would not intervene due to its focus on Europe and recent engagements in WWII. US intervention was prompted by the imperative to maintain its credibility in combatting Communism. Nevertheless, Stalin provided support such as weaponry and advisors, without committing Soviet troops directly.
Step-by-step explanation:
The reason why Stalin encouraged Kim Il-sung to start the Korean War was mainly based on Kim Il-sung's own belief that the United States would not intervene. Stalin himself did not wish to engage directly in a confrontation with the US over Korea, and the Soviet Union did not send troops to assist North Korea at the outset, though the North Koreans were supplied with Soviet weaponry and advisors.
The Korean War was, in part, influenced by the perception of a US focus on Europe over Asia and the recent Communist victory in China, which lent urgency to the containment efforts in Korea.
Stalin believed that Kim's forces, with Soviet arms, could successfully reunify Korea under communist rule without triggering direct US military response based on America's primary focus on Europe and recent involvement in World War II.
However, the United States did intervene, as the fall of South Korea to Communism would have raised questions about the US commitment to combating Communist expansion during the Cold War. Kim Il-sung's government also played on fears of capitalist and communist spread to secure Soviet backing. Subsequent developments, including the participation of China on the side of North Korea, further complicated the conflict.