"After 1870 Marx became convinced that a peaceful transition to communism was possible as long as certain objective and subjective conditions were present. The required objective conditions were the existence of a strong proletarian class, which assumes a high degree of capitalist development, and the existence of a strong democratic tradition and political institutions, denoted in part by suffrage and its possible expansion by peaceful agitation and organization on the part of the organized proletariat. The subjective condition was the presence of an organized workers’ or communist movement. These conditions being present, any agitation for a revolution would not only be unnecessary, but even counterproductive and foolish."
This article gives a pretty thorough and well cited account of the evolution of his thought on this subject.