Yoshitaka Shindo, the minister of internal affairs and communication, visited Yasukuni shrine on New Year's Day as thousands of people attended Shinto shrines and Buddhist temples to pray for good fortune in 2014, Jiji and Kyodo news agencies said.
Last Thursday Abe made his first visit as premier to Yasukuni shrine, which honours Japan's war dead including several high-level officials executed for war crimes after World War II.
China and South Korea see it as a brutal reminder of Tokyo's imperialist past and wartime aggression.
He previously served as premier from 2006 to 2007 without visiting Yasukuni after his predecessor Junichiro Koizumi's repeated pilgrimages there saw ties with Beijing and Seoul plunge to their worst in decades.
While prime ministers after Koizumi have refrained from going to the shrine, conservative lawmakers regularly offer prayers there for the war dead.