Abe said he would work closely with other countries in the region including China and Russian Federation to persuade North Korea to halt missile development and give up its nuclear weapon ambitions.
North Korea has continued to beef up its nuclear program despite UN Security Council sanctions and widespread condemnation by the global community.
Japan, along with neighboring South Korea, stand as those most in danger from a North Korean missile or military attack.
Abe's stance appears to largely mirror Trump's.
"In the 50 years ahead, we want to lead together with ASEAN, which faces both the Indian and Pacific oceans, the development of a free and open worldwide order based on the rule of law, building on (ASEAN's) development so far", Abe said. "Japan has no choice but to strengthen cooperation with the United States".
World leaders who attended a regional summit here shared an "unprecedented sense of crisis" over North Korea's continuous development of nuclear weapons, Japanese Prime Minister Shinzo Abe said Tuesday.
Japan's foreign minister Taro Kono last month had said that Tokyo favours the quadrilateral dialogue to further boost strategic partnership among the four countries. Five of the 17 were repatriated in 2002.
Abe said Japan will now cooperate with China and Russian Federation - 2 of North Korea's major trading partners - to closely watch Pyongyang.
Duterte said that North Korean leader Kim Jong Un should realize that he would be responsible if nuclear activities in his country would cause the world's destruction. The talks marked their first since a September meeting in western India and the 11th overall as prime ministers.
North Korea responded by launching another ballistic missile over Japan on September 15.
'We are working very closely together.
But asked at the press conference later about how to rescue the abductees if war breaks out on the Korean Peninsula, Trump stopped short of giving a clear answer, saying, "We'll see what happens in terms of the ultimate conclusion".
"I can assure you that in the matter of the interest of your country and mine, we are supporting you against what North Korea is doing", Duterte told Abe.
"With the North Korea situation at an important phase, the role China ought to play is very big", Abe said.
North Korea, however, repeatedly postponed reporting the survey results.