The Paracel and Spratly Islands, known as the Hoang Sa and Trong Sa islands in Vietnam, are in the South China Sea, a busy global maritime waterway almost all of which is claimed by China. Vietnam, Malaysia, the Philippines, Taiwan and Brunei are among other claimants.
Vietnam has "full legal basis and ample historical evidence" to assert its sovereignty over the two island chains, its foreign ministry said on Saturday, in response to a query from the media on China's "invasion" of the Paracel Islands in 1974.
"Viet Nam's sovereignty over the Hoang Sa Islands has been established since at least the 17th century in accordance with international law, and exercised in a peaceful, continuous and public manner by successive Vietnamese states," it said.
But the Chinese foreign ministry said China's claims are "fully supported by history and jurisprudence."
"China was the first to discover, name, develop and manage these islands and archipelagos, and continue to exercise sovereign jurisdiction over them," said Wang Wenbin, a Chinese foreign ministry spokesperson, at a regular news conference.
"China always opposes relevant countries' illegal claims on China's territory and will continue to firmly safeguard its sovereignty."
Vietnam's re-assertion of its claims coincides with months of vigorous claims by the Philippines in other parts of the South China Sea after dramatic maritime encounters between Chinese and Philippine vessels near disputed territory.
In December, Chinese President Xi Jinping visited Vietnam and sealed an agreement to move towards the building of a community with a "shared future" between the two countries.