The so-called freedom-of-navigation patrols were reported earlier Monday by Reuters, which cited an unidentified USA official.
Doss confirmed the sailings to CNN.
Washington has hit back in the past, claiming it is countering Beijing's militarisation of the South China Sea by building army installations on artificial reefs and islands.
Last year, China added surface-to-air missiles to the contested island, one of three that the Chinese military fortified in 2018.
Global waters are considered 12 nautical miles from land. "We've got big interests there, so we're going to remain there", Adm. John Richardson, the chief of naval operations, said recently.
Doss said FONOPS "are not about any one country, nor are they about making political statements".
On Monday, Chinese foreign ministry spokeswoman Hua Chunying said its Navy warned the ships against approaching Chinese-claimed territory in the Spratly Islands.More news: Apple, VA to let veterans access their health records on iPhone
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It was the second such U.S. operation in the South China Sea this year.
She demanded the United States "immediately stop its provocative actions" after the two destroyers conducted what Washington called "freedom of navigation" exercises in the area.
In January, the destroyer USS McCampbell sailed within 12 nautical miles of the Paracel Islands. The report said two guided-missile destroyers passed within 12 nautical miles of Mischief Reef, a maneuver the US uses to assert that a waterway is free to worldwide transit.
China has criticized both encounters.
During an interview Monday, White House Counselor Kellyanne Conway said the president wants to meet with President Xi very soon.
In September, a Chinese warship came within just 45 yards of a US destroyer, raising concerns about the possibility of tensions boiling over into conflict. Other regional nations-such as the Philippines and Vietnam-lay claim to part of the waterway and the USA routinely pushes back against China by sending ships to patrol the sea.
The two sides are trying to hammer out a deal ahead of a March 1 deadline when USA tariffs on US$200 billion (S$272 billion) worth of Chinese imports are scheduled to increase to 25 per cent from 10 per cent. Mr Lighthizer, named by President Donald Trump to spearhead the process after agreeing a 90-day truce in the trade war with Beijing, has been a strong proponent of pushing China to end what the U.S. views as unfair trade practices, including stealing intellectual property and forcing United States companies to share their technology with Chinese firms.