Separately, China's Maritime Safety Administration said on Monday that an area just off the east of the island province of Hainan would be a no-sail zone from July 19-21 while military drills take place.
The announcement came during a three-day visit to China by US Chief of Naval Operations Admiral John Richardson to discuss the South China Sea dispute and ways to increase interaction between the two militaries, which continue to have tense ties.
The Chinese government has also strongly warned other countries against the danger of the South China Sea, "a war cradle".
Half of the 10 ASEAN countries have some sort of South China Sea dispute with Beijing, but China's ally Cambodia said it does not want the bloc to mention the ruling.
Heydarian says that mistrust of US support helps explain the Philippines' tempered response to the court's verdict.
While prodding China to "respect" the decision, Calida said the government would deal with Beijing diplomatically to foster better relations.
"We highlighted how useful and beneficial those areas but on the other hand we didn't dodge the more contentious issues, the more solemn issues as the Chinese would say regarding disposition in the South China Sea, the recent court of arbitration ruling and those issues as well, recognizing that it's only through being completely frank and honest that we're going to make any kind of progress on these areas".
China refused to take part in the tribunal, initiated by the Philippines, saying that islands in the South China Sea are "China's inherent territory".
China claims most of the energy-rich waters through which about $5 trillion in ship-borne trade passes every year.
Under a 1982 United Nations treaty governing the world's oceans, the Philippines had sought arbitration in 2013 on several issues related to territorial rifts with China.
However, the global tribunal sided with the Philippines in ruling China's claimed historic rights to resources within the so-called nine-dash line had no legal basis.
China defiantly announced Monday it will militarily close off parts of the South China Sea to conduct war drills, a week after an worldwide tribunal denied China's historic claims to the majority of the region.
Their latest conversation, in January, touched on China's new airport on Yongshu Reef in the Nansha Islands, which was put into use that month.
China will not leave outcroppings under construction half finished, state-run Xinhua news agency reported People's Liberation Army Navy Chief Admiral Wu Shengli as saying.
Japanese Foreign Ministry spokesman Yasuhisa Kawamura said Abe "reiterated the fundamental positions regarding the South China Sea" in his meeting with Li.
The UN tribunal ruled that China violated worldwide maritime law, specifically the Philippines' maritime rights by building up artificial islands that destroyed coral reefs and by disrupting fishing and oil exploration.
Similarly, the Pentagon has deployed B-52 bombers over the South China Sea, citing "freedom of navigation".
Several times in the past year, US warships have deliberately sailed close to one of those islands to exercise freedom of navigation and challenge the claims.
It will be detrimental to all sides if the South China Sea dispute is allowed to further fester, lead to provocative and antagonistic rhetoric and posturing from within the region and beyond and, worse, result in conflict.
Beijing has repeatedly blamed the United States for stirring up trouble in the South China Sea, where its territorial claims overlap in parts with Vietnam, the Philippines, Malaysia, Brunei and Taiwan.