WASHINGTON — The escalating brinkmanship between the United States and China as they race to quash each other’s global influence is forcing other nations to pick sides between the two superpowers, putting at risk future cooperation on geopolitical threats and a resolution to the economic standoff.

The rivalry, which has reached a new pitch and scope, is now centered on the trade war that President Trump started this year. But tensions have also sharpened over a broad range of diplomatic and military issues, like Taiwan, the South China Sea and economic sanctions on North Korea and Iran.

Across the globe, the United States and China are jockeying to build alliances or partnerships and shut out the other power. The hard-nosed competition surfaced over the weekend at an Asian economic forum that pitted Vice President Mike Pence against President Xi Jinping of China. The dispute threatens to disrupt the Group of 20 summit meeting that starts Nov. 30 in Argentina.

The United States again vented its frustration on Tuesday, accusing China of continuing to engage in unfair trade practices despite Mr. Trump’s tariffs. “China fundamentally has not altered its acts, policies and practices related to technology transfer, intellectual property and innovation, and indeed appears to have taken further unreasonable actions in recent months,” the Office of the United States Trade Representative said in a report.