**Shares of copper miners rise, tracking gains in red metal prices MET/L

** Benchmark three-month copper on London Metal Exchange CMCU3 up 0.4% at $13,218 per metric ton, after touching a record $13,407 earlier in the session

** Prices rise on persistent demand from speculative funds, but some investors wary that rally will deter industrial buying

** U.S.-listed shares of global mining giants: Rio Tinto RIO.N up 2.5%; BHP Group BHP.N gains 2.3%

** Southern Copper SCCO.N gains 2.6%; Freeport-McMoRan FCX.N up marginally

** Canadian miners: Teck Resources TECKb.TO up 2.2%; Hudbay Minerals HBM.TO gains 1.4%

(Reporting by Sumit Saha in Bengaluru)

((Sumit.Saha@thomsonreuters.com;))