Russia is seeking to interfere in countries across southeastern Europe, the leaders of Germany and Georgia said Monday, highlighting rising Western fears that the Ukraine conflict is spilling over into a broader Cold War-style effort by Russia to assert influence abroad.

During a visit to Australia, German Chancellor Angela Merkel rebuked Moscow in unusually harsh language for “old thinking in terms of spheres of influence in which international law is trampled upon.” In an interview in Brussels, Georgian Prime Minister Irakli...