Tokyo and Beijing have long been at odds over islands in the East China Sea with simmering distrust flaring more recently after Japan moved to loosen the bonds on its powerful military.
Abe was in Canberra today where he and counterpart Tony Abbott were expected to sign an agreement on closer defence ties, a move that could further anger China.
In an interview with The Australian broadsheet, Abe said he was keen to nurture a mutually beneficial relationship with Beijing, while urging China to play a constructive role in regional security.
"China is a major country which, together with Japan and Australia, has to play a prominent role in ensuring the peace and prosperity of the Asia-Pacific region.
"It is my strong expectation China will abide by international norms and play a constructive role in dealing with regional issues.
"In accordance with the principle of a mutually beneficial relationship based on common strategic interests, I would like to develop relations with China in a way that keeps a broad perspective.
China last week lashed out at Abe after his cabinet formally endorsed a reinterpretation of a constitutional clause banning the use of armed force except in very narrowly-defined circumstances.
Beijing argued that it could open the door to remilitarisation of a country it considers insufficiently penitent for its actions in World War II.
Tensions also continue to simmer over the hotly contested Japanese-controlled Senkaku islands in the East China Sea, which China also claims and calls the Diaoyus.
During his visit to Australia, Abe was due to attend a meeting of the cabinet-level National Security Committee in Canberra and address parliament, the first Japanese leader to do so.
