John Kennedy actually said...
The Communists have a strategy for world conquest and that strategy rests in the future, as it has in the past, on the use of every weapon of economic and ideological conflict to win the allegiance of the uncommitted nations of the world and increase their dependence on the support of the Soviet Union,
Context
Excerpts of Speech by Senator John F. Kennedy, American Legion Convention, Miami Beach, FL - (Advance Release Text)
10/17/1960