"Japan is willing to cooperate with any country to support this concept with Malaysia. I am resolved to further strengthening cooperation for regional peace and stability, including in the maritime safety area," he said at a joint press conference with visiting Malaysian Prime Minister Tun Dr Mahathir Mohamad in Tokyo.
The press conference was broadcast live over national television and the social media.
Dr Mahathir is on a three-day working visit to Japan, his first trip overseas since taking office as Malaysia's seventh prime minister following a stunning election victory by the Pakatan Harapan coalition on May 9.
At the joint press conference, Dr Mahathir said: "We agreed that we should keep the Strait of Melaka and the South China Sea for navigation for all countries.
After the event, Abe presented Dr Mahathir with a Japan World Cup team jersey with Dr Mahathir's name and the number 7 printed on it to symbolise him being the seventh prime minister of Malaysia.
Abe said the gift also marked the wish for further friendship between the two nations.
Dr Mahathir presented Abe with a book on himself, and said it would enable Abe to know him better.