A new and distinct Echeveria cultivar named ‘AMIECH1604’ which is characterized by a fast rate of growth, improved winter hardiness, and a flattened globular plant shape with thick, robust foliage with a broad obovate to spatulate shape which is arranged in a compact rosette. The juvenile foliage towards the center of the rosette exhibits a pink to red general coloration with pink margins, and mature foliage towards the outer whorls of the rosette that exhibits a red-purple general coloration with greyed-red margins. The new variety has shown to be uniform and stable in the resulting generations from asexual propagation.
