Burke River (New Zealand)  The Burke River is a river of New Zealand's South Island, located in Mount Aspiring National Park. It flows east for from close to the Mueller Pass, reaching the Haast River south of the Haast Pass. The river was named by Julius von Haast when he searched for a crossing from Otago to the West Coast. It is named for Robert O'Hara Burke of the Burke and Wills expedition. The nearby Wills River is named for William John Wills.