Extinction characteristics of stretched premixed flames have been numerically investigated by adopting a detailed chemistry in an axisymmetric counterflow for various fuels. The Karlovitz number, defined as the ratio of the characteristic one-dimensional reaction time for an unstretched premixed flame to the characteristic flow time of the inverse of flame stretch rate, exhibited large spread at extinction conditions. To test a universal extinction criterion that can be applied irrespective of fuel type, equivalence ratio, pressure, and initial temperature, a local Karlovitz number was defined as the ratio of the local reaction time to the characteristic flow time of stretched flames. The result showed that the local Karlovitz number based on the flame thickness at extinction can be reasonably approximated as 1.1, irrespective of equivalence ratio for the fuels tested including alkane (methane and propane), alkene (ethylene), alkyne (acetylene), alcohol (methanol), and hydrogen. By analyzing existing experimental data for premixed flames of methane and propane, the measured local Karlovitz numbers at extinction have also been found to have a near constant value. The local Karlovitz number was relatively insensitive to pressure variation up to 10 atm and initial temperature up to 1000 K. The present results implied that extinction occurs when the ratio of the characteristic flow time to the local characteristic reaction time exceeds a near constant value for the fuels tested irrespective of equivalence ratio, pressure, and initial temperature.