Many other countries, however, have not chosen sides. They are willing to work closely with both Washington and Beijing, depending on the issue. These countries tend to be flawed democracies (like Brazil, India, Israel and Nigeria) or autocracies (like Saudi Arabia and Vietnam). If the U.S. suggests that only democracies are welcome in its alliance, that alliance will shrink.

“Defining the current contest as one between democracies and autocracies is a flawed strategy,” Walter Russell Mead, a foreign policy expert at the Hudson Institute, wrote in The Wall Street Journal this spring. “Abroad, this approach weakens America’s ties with key allies and exposes us to devastating charges of systemic hypocrisy.” Mead is a conservative who often criticizes Biden, but some members of the administration have had similar concerns, as Peter Baker, The Times’s chief White House correspondent, has reported.

In June, Jake Sullivan, Biden’s national security adviser, acknowledged the tension. “I do think we are dealing with the gathering and march of autocratic forces in ways that are not in the United States’ national interest, and that we do need to rally the values, norms and forces of democracy to push back against that,” Sullivan said. But, he added, Biden “has also been clear that in that larger effort, we need constructive relationships with countries of all different traditions and backgrounds.”

The C.I.A. and Stalin

There is, of course, a long history of the U.S. working with autocracies as part of a stated strategy of fostering democracy. Sometimes, this history has been tragic, as during the Vietnam War. Other times, the practice has aged well, such as the alliances with Stalin’s Soviet Union during World War II or with Persian Gulf kingdoms to evict Saddam Hussein from Kuwait during the 1990s.

The democracy-vs.-autocracy dichotomy has probably been most helpful in energizing Western Europe to come to Ukraine’s defense and persuading Japan and South Korea to strengthen ties as a counterweight to China. Over the past year, though, the administration has also tried to build ties with countries that are democratically weaker:

• India is another potential counterweight to China, and Biden hosted its prime minister, Narendra Modi, for a warm three-day visit this year despite Modi’s crackdown on critics of his Hindu nationalist government. (This week, Justin Trudeau, Canada’s prime minister, accused India’s government of killing a Sikh separatist leader in British Columbia.)

• The U.S. strengthened its ties with Vietnam — which remains a one-party state — when Biden visited Hanoi this month. Both countries are worried about China’s ambitions.

• Turkey, Hungary and Poland are important parts of the alliance supplying Ukraine with weapons to fight Russia.

• The Biden administration is talking with Saudi officials about establishing a mutual defense treaty in which each country would promise to come to the other’s aid if attacked, my colleagues Edward Wong and Mark Mazzetti reported yesterday. The talks are part of an effort to persuade Saudi Arabia and Israel to normalize their relations.

All of this may help explain the approach Biden took at the U.N. yesterday. He continued to celebrate the virtues of democracy, saying that it “can deliver in ways that matter to people’s lives” while describing programs to build infrastructure in Africa, Latin America and Southeast Asia. Yet he did not use any versions of the words “autocracy” or “authoritarian.”