MOSCOW—Russian President Vladimir Putin on Tuesday told the new U.S. ambassador to Moscow he hoped Washington would follow a policy of “noninterference” in the country’s domestic affairs, amid the ongoing controversy over alleged Russian interference in the 2016 U.S. election.

Mr. Putin accepted credentials from U.S. Ambassador Jon Huntsman, a former Utah governor and envoy to China and Singapore, in a ceremony at the Kremlin. In remarks to newly arriving diplomats, Mr. Putin said the basis for cooperation between Moscow and...