Motivated by the idea and examples of Kramosil-Michalek fuzzy metric we develop an alternative approach to the concept of a fuzzy metric. It is obtained by fuzzy extension of a crisp metric d on a set X by means of a fuzzy equivalence relation E on the set R+. We call it an Extensional Fuzzy Metric and study its properties and relations with "classical" fuzzy metrics. Our special interest is in topologies and fuzzy topologies induced by extensional fuzzy metric.