Strategy for the region, in Washington and Beijing, revolves around how each country can assert military dominance in the Pacific. For now, the most powerful military in the region is still that of the United States, which relies on the ability to have unfettered naval access to the South China Sea and the support of the self-governing island of Taiwan to bolster its standing.

But China has become more aggressive in trying to assert dominance over both. And its state-owned companies are making inroads in the islands of Oceania — from Saipan to Vanuatu — with infrastructure projects. American officials say those could eventually become beachheads for the People’s Liberation Army, which would pose a challenge to the United States Navy’s operational command in the far island chains. Australia is also watching closely because the South Pacific has traditionally been its sphere of influence.

Closer to home, China has continued to place military equipment and installations on rocks and reefs in the South China Sea, over which it claims sovereignty. And it is persuading some nations to sever diplomatic ties with Taiwan while forcing foreign companies, including hotels and airlines, to drop any mention of Taiwan.

There is a consensus in Washington that American officials need to find ways of pushing back.

In the South China Sea, that has mainly taken the form of what are called freedom-of-navigation operations by the Navy, in which ships sail near the islands or features claimed by Beijing to establish that the waters are international — and not Chinese territory. On Sept. 30, American and Chinese warships nearly collided, coming within 45 yards of each other.