Branching fraction and asymmetry measurements of charmless B+→K*+h1+h2- (where h1,2=K, π) decays are presented, using a data sample of 232×106 Υ(4S)→BB̄ decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy B factory. Using a maximum likelihood fit, the following branching fraction results were obtained: B(B+→K*+K+K-)=(36.2±3.3±3.6)×10-6 and B(B+→K*+π+π-)=(75.3±6.0±8.1)×10-6. Upper limits were set for B(B+→K*+π+K-)<11.8×10-6 and B(B+→K*+K+π-)<6.1×10-6 at 90% confidence level. The charge asymmetries for the decays B+→K*+K+K- and B+→ K*+π+π- were measured to be AK*KK=0.11±0.08±0.03 and AK*ππ=0.07±0.07±0.04, respectively. The first error quoted on branching fraction and asymmetry measurements is statistical and the second systematic. © 2006 The American Physical Society.