What policy declared that future conflicts in Asia would be supported by weapons and not with American troops?

The policy referred to is the "Eisenhower Doctrine," announced in 1957. It aimed to provide military and economic assistance to Middle Eastern countries resisting communist aggression, emphasizing the use of U.S. weapons and support rather than deploying American troops. This doctrine marked a shift in U.S. foreign policy, focusing on containment through indirect means rather than direct military intervention.