Why did Austria join Prussia in the war against Denmark?

Austria joined Prussia in the German-Danish War of 1864 primarily to uphold international agreements and maintain its influence within the German Confederation.

When the Danish government attempted to integrate the duchy of Schleswig more closely into the Danish state in 1863, it violated previous international protocols that guaranteed the autonomy of the duchies. Prussia proposed a joint occupation of the territories to address this violation. Austria, fearing that Prussia would act unilaterally and thereby strengthen its own position at the expense of Austrian influence, agreed to participate in the intervention.12

Furthermore, Austrian participation was motivated by a desire to thwart Prussian ambitions regarding the future of the duchies. By acting as a joint power, Austria sought to ensure that any settlement would align with its own interests—specifically, preventing the outright annexation of the territories by Prussia and maintaining the balance of power between the two leading German states.32