The United States has reportedly deployed carrier strike groups for drills in the contested South China Sea as it ramps up its opposition to Beijing’s maritime claims in the region.

The USS Carl Vinson and USS Essex, a Wasp-class Landing Helicopter Dock – along with their escort vessels – entered the southern waters of the sea on Tuesday, said Beijing-based think tank, the South China Sea Strategic Situation Probing Initiative.

According to the South China Morning Post, the US Navy is expected to conduct joint drills in the strategic international waterways, whose islands, atolls and reefs are subject to territorial disputes between China and several Southeast Asian nations including the Philippines and Vietnam.

The exercises have so far not been confirmed by the United States Navy.

On Wednesday, the US State Department laid out its most detailed case yet against Beijing’s “unlawful” claims in the South China Sea, rejecting its geographical and historical assertions, and calling on China to cease its “coercive activities.”

In a 47-page research paper, the State Department’s Bureau of Oceans and International Environmental and Scientific Affairs said China had no basis under international law for claims that have sparked frequent clashes between Beijing and other regional capitals.

“The overall effect of these maritime claims is that the PRC [People’s Republic of China] unlawfully claims sovereignty or some form of exclusive jurisdiction over most of the South China Sea,” the paper said.

“These claims gravely undermine the rule of law in the oceans and numerous universally recognised provisions of international law,” it said.

In 2016, the UN-backed permanent court of arbitration in the Hague ruled in favour of a complaint from the Philippines over China’s claims, saying that Beijing “had no historic rights to resources in the waters of the South China Sea.” China has refused to accept this verdict.

The latest State Department report objects to Chinese sovereignty claims over more than a hundred features in the South China Sea and to its claimed maritime zones, disputing the so-called “nine-dash line” that forms the basis for much of Beijing’s stance.

The South China Sea is rich with oil and gas deposits and is crucial for international shipping. Beijing’s increasing swagger in the region has prompted alarm and a growth in “freedom of navigation” operations by the US and its allies.

On Thursday, Japanese newspaper, the Yomiuri Shimbun, reported that Japan had conducted two of its own operations last year through waters near the artificial islands and reefs claimed by Beijing, “to warn China.”