The KKK was heavily connected to the Democratic party. At the very same time the Republicans were looking to abolish slavery.
PBS wrote:the Klan quickly became a terrorist organization in service of the Democratic Party and white supremacy. Between 1869 and 1871 its goal was to destroy Congressional Reconstruction by murdering blacks -- and some whites -- who were either active in Republican politics or educating black children.
Read more: http://www.pbs.org/wnet/jimcrow/stories_org_kkk.html