US Defence Secretary Chuck Hagel has urged Japan to improve relations with neighbouring countries after Prime Minister Shinzo Abe's visit to a controversial war shrine, an American official has said.

Abe enraged China and South Korea when on December 26 he 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.

"Secretary Hagel underscored the importance of Japan taking steps to improve relations with its neighbours, and to promote cooperation in advancing the shared goals of regional peace and stability," Pentagon press secretary John Kirby said in a statement posted on the US Defence Department website late Saturday.

The comments were issued after telephone talks between Hagel and Japanese Defence Minister Itsunori Onodera.

China and other Asian countries say the shrine serves as a reminder of Japan's 20th century aggression, and is a source of bitterness between Japan and its neighbours and Abe's visit also sparked criticism from Washington.

During their conversation late Saturday, Onodera sought Hagel's understanding over the visit, telling his counterpart that the prime minister had renewed Japan's pledge that it must never wage war again, Kyodo News said citing Japanese officials.

Hagel had also thanked the Japanese government for its efforts in securing approval from Okinawa's governor to move towards relocating a US Marine Corps air base on the island, Kirby said.