McCartney was quoted as saying it was he who first raised concerns over the Vietnam war within the group and advocated their anti-war stance.
Fans have long regarded Lennon, who wrote songs such as "Revolution" and - in later years - "Give Peace a Chance," as the group's authentic political voice.
But McCartney claimed that his meeting with philosopher Bertrand Russell in the mid-1960s sparked his own - and eventually Lennon's - curiosity about world affairs.
Following his talk with Russell, McCartney said he told "the guys, particularly John (Lennon), about this meeting and saying what a bad war this was," The Sunday Times quoted McCartney as saying in the interview.
The newspaper said McCartney was interviewed in Britain's Prospect magazine, which is published on Wednesday. McCartney's publicist Stuart Bell was not immediately available to confirm the comments.
According to the newspaper, McCartney said he believes his stance has inspired the work against African poverty carried out in recent years by Bob Geldof and U2's Bono.