"We have said it several times already in the past that it is not [in] the interest of North Korea to swagger around and threaten the world, of keeping us hostage with the atomic weapons", the Philippine president added.
Mr Turnbull and Mr Trump are in Manila for the ASEAN Summit, and fronted media together with Japanese Prime Minister Shinzo Abe on Monday.
The Philippines is hosting the 31st Association of Southeast Asian Nations (ASEAN) Summit and Related Meetings from November 10 to 14.
"Nuclear and missile issues of North Korea is a grave and imminent threat that we have never experienced", Abe said during the 20th ASEAN-Japan Summit held on Monday. He has declared deep admiration for President Rodrigo Duterte, whom he visited at his Davao home when he flew in for a two-day official visit last January.
"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 global order based on the rule of law, building on (ASEAN's) development so far", Abe said.
In response to the rising threat of terrorism in Asia, Abe said Japan continues to assist ASEAN nations in the domain of terrorism and violent extremism as it assists the Philippines in the rehabilitation of Marawi City.
Abe and the Mekong leaders also confirmed their cooperation in improving conditions in Myanmar's Rakhine State, where violence has sparked an exodus of more than 600,000 Rohingya Muslim refugees.
In the area of partners for prosperity, Abe said he wishes to promote free trade by clearly presenting the importance of free and open trade and investment.
'This has been a very fruitful trip for us and also in all fairness for a lot of other nations, the way they've treated us, the respect that Japan and China and South Korea... have treated us has been really a great respect for the people of our country... and we very much appreciate it'.
"We need to use every means, including the complete implementation of the (U.N.) Security Council resolutions, to raise pressure on North Korea to the maximum possible extent and make it change its policies", Abe said at the outset of the talks.
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