WASHINGTON — Senator Saxby Chambliss, a Georgia Republican who helped lead efforts to find a bipartisan deficit reduction compromise, announced Friday that he would retire at the end of 2014, a decision likely to set off a battle on the Republican Party’s right flank for a successor.

Already, organizations backed by the Tea Party movement were stirring interest in a primary challenge for Chambliss over his embrace of new revenues as a part of any comprehensive deficit package. Representatives Tom Price and Paul Broun, two Republican doctors and ardent conservatives from Georgia, had expressed interest in a possible challenge.