Duterte's rivals have likened his refusal to insist that China abide by the ruling as akin to surrendering sovereignty.
The Philippines and China played down on Monday a warning by President Rodrigo Duterte that China would go to war if the Philippines drilled for oil in the disputed South China Sea.
The outspoken Philippine president has been facing criticism at home for being what some people see as too soft on China over a long-running territorial dispute.
Duterte met China's President Xi Jinping for talks in Beijing last week and later said Xi had warned him there would be war if the Philippines tried to explore for oil in a disputed stretch of sea.
Foreign Secretary Alan Peter Cayetano said their meeting was frank and friendly, and the discussion was largely about preventing conflict, not threatening it.
"The conversation was very frank. There was mutual respect, there was mutual trust," Cayetano told reporters.
"The context was not threatening each other, that we will go to war. The context is how do we stabilise the region and how do we prevent conflict."
He added: "I will not contradict the president's words. I am just telling you ... my interpretation: there was no bullying or pushing around, it was not a threat."
Speaking in Beijing, Chinese Foreign Ministry spokeswoman Hua Chunying also sought to make light of Duterte's comments, noting he and Xi had agreed to "strengthen communication" on important bilateral issues.
China was willing to work with the Philippines to handle disputes peacefully, she told reporters. Duterte made no mention of the issue during an unusually news briefing on Monday before he left for Russia.
Duterte's critics have made much of his refusal to push China to comply with a ruling last year by the Permanent Court of Arbitration in The Hague, at the end of a case brought by the Philippines against China, which was largely in favour of the Philippines. China has never recognised the case.
The court said the Philippines had a sovereign right to access offshore oil and gas fields in its Exclusive Economic Zone. Duterte's rivals have likened his refusal to insist that China abide by the ruling as akin to surrendering sovereignty.
Senate minority leader, Frank Drilon, said the government "should not allow our country to be bullied and threatened," while former foreign minister Albert del Rosario said Manila should do joint maritime patrols with traditional ally the United States, an idea he said Duterte had jettisoned as part of his "full embrace of China".
Duterte chafes at what he considers Philippine subservience to the United States and has sought to engage more with China, which has promised loans and investment that will be vital to his ambitious $180 billion infrastructure overhaul.
Supreme Court Associate Justice Antonio Carpio on Saturday urged the government to file another international arbitration case over the reported Chinese threat, and also lodge a complaint with the United Nations.
Presidential Spokesman Ernesto Abella said the Philippines was "very clear that we are not giving up our claim of sovereignty and sovereign rights".
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 "China, Rodrigo Duterte, Philippines, Beijing, United States, Albert del Rosario")
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