05 July, 2017
Fox News, which first reported on Sunday's incident, said a Chinese warship tailed the Stethem as it sailed past the island, although it is unclear how close the ship came to the American vessel.
The North Korea problem remains as clear as ever.
Chinese President Xi Jinping told U.S. counterpart Donald Trump on Monday that bilateral relations were "affected by some negative factors", state media said following a series of USA actions that angered Beijing.
There was a more positive tone in the Xinhua story when it quoted Mr Xi saying that "important results have been achieved in bilateral relations" between China and the USA since the Mar-a-Lago meeting between the two leaders.
Mr Trump encouraged warmer relations with Mr Xi as he sought to enlist his assistance in encouraging China's allies in Pyongyang to abandon their nuclear ambitions.
Observers warned that if Washington fails to do damage control, ties between the countries may fray, as an arms deal breaches U.S.pledges in past official statements and betrays the one-China policy.
The broadcaster did not identify specific issues discussed in the call.
"Both leaders reaffirmed their commitment to a denuclearized Korean Peninsula", the White House said in a readout of the phone call.
As Donald Trump told the story, his relationship with President Xi Jinping of China reached its climax at the end of a dinner.
China hopes that the United States will handle the Taiwan issue appropriately in accordance with the one-China principle and the three China-U.S. joint communiques, Xi said.
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"I don't see that alone as a provocation towards China, rather I think if we connect up these other areas, including sanctions on Chinese entities, that's the thing to watch". He pronounced his intention to cooperate with Japan and South Korea to increase pressure on North Korea by enforcing sanctions.
In exchange for Xi's agreement to help restrain North Korea, the Trump administration loosened or withdrew U.S. pressure in other areas, including the South China Sea and Trump's previous campaign pledge to label China a currency manipulator.
Another issue causing tension between Washington and Beijing is Chinese expansion in the South China Sea.
Seeking to lighten the message slightly, Xi also said that China-U.S. relations had achieved "important outcomes" since the Florida meeting.
In the latest sign of tension, a USA naval destroyer on Sunday sailed near disputed territory claimed by Beijing in the South China Sea, prompting a furious response from the Chinese government.
Beijing claims nearly the entire south China sea, and administers several islands in the area.
US officials said the Navy's action, known as a freedom-of-navigation operation, or FONOP, was planned in advance and was not targeted at any one country, nor aimed at making a political statement. It added that such operations "violate China's sovereignty and threaten China's security". The operation within 12 nautical miles of the island was meant to show that the USA does not recognize territorial claims to the island.
The 12-mile line is the internationally recognized distance that separates the shores of a sovereign nation from worldwide waters.
US President Trump also spoke to Japanese Prime Minister Shinzo Abe by phone, with the two pledging deeper cooperation on North Korea, in the wake of growing frustrations over the rogue state.