WASHINGTON—The Obama administration Wednesday urged the Supreme Court to reject a challenge to Colorado’s 2012 marijuana initiative filed by Nebraska and Oklahoma officials, who say legalization has increased drug crimes in their states.

U.S. Solicitor General Donald Verrilli in a legal brief said: “Entertaining the type of dispute at issue here—essentially that one state’s laws make it more likely that third parties will violate federal and state law in another state—would represent a substantial and unwarranted expansion”...