According to the Vietnamese foreign ministry, the airfield was built illegally on a part of the Spratly archipelago that lies within its territory.
China said it has complete sovereignty over Fiery Cross Reef and had used a civilian plane to test the airstrip.
Several nations dispute China’s territorial claims in the area.
China claims almost the whole of the South China Sea, resulting in overlapping claims with several other Asian nations including Vietnam and the Philippines.
They accuse China of illegally reclaiming land in contested areas to create artificial islands with facilities that could potentially be for military use.
The US has said it was concerned that January 3 flight had exacerbated tensions.
Pooja Jhunjhunwala, a spokeswoman for the US State Department, said there was “a pressing need for claimants to publicly commit to a reciprocal halt to further land reclamation, construction of new facilities, and militarization of disputed features”.
“We encourage all claimants to actively reduce tensions from unilateral actions that undermine regional stability, and taking steps to create space for meaningful diplomatic solutions to emerge,” Pooja Jhunjhunwala said.
Chinese foreign ministry spokeswoman Hua Chunying said China conducted the flight to test whether the airfield facilities met the standards for civil aviation.
“China has indisputable sovereignty over the Nansha Islands and their adjacent waters. China will not accept the unfounded accusation from the Vietnamese side,” Hua Chunying said, referring to the Spratly Islands by their Chinese name.
Hanoi’s foreign ministry said Vietnam handed a protest note to China’s embassy and asked China not to repeat the action, Reuters reported.
It called the flight “a serious infringement of the sovereignty of Vietnam on the Spratly archipelago”.
Satellite images published in April 2015 showed China making progress with building the airstrip on reclaimed land on Fiery Cross Reef in the Spratly Islands.
The landmass could accommodate a runway about 3,000m long.
It also showed dredging to the south of the reef, in apparent work to improve the reef’s port facilities.
China says its work is legal and needed to safeguard its sovereignty.
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