Mayor Thomas M. Menino on Monday for the second time vetoed a redistricting proposal passed by the City Council, concerned that the latest version would still dilute the voting power of communities of color.

The measure was narrowly approved by the council last week after a surprise parliamentary maneuver forced a vote on a proposal that had languished for months. The new map included just a handful of changes from the first proposal Menino rejected, and did not address the mayor’s paramount concern.