The cables, released last week by the Web site, were published by Kommersant on Monday, The Moscow Times reported.
A cable from 2009 alleges Putin holds a grudge against Estonia because Estonian locals handed his father, a member of the Red Army who had parachuted into the country during World War II, over to Nazi forces. His father managed to escape but was injured, the report said.
Putin had no comment on the cable, which had been marked confidential by U.S. Ambassador to Estonia Michael Polt, the newspaper said.