Mr. Obama is returning to Asia as Russia pulls closer to China, presenting a profound challenge to the United States and Europe. Estranged from the West over Ukraine, Mr. Putin will also be in Beijing this week as he seeks economic and political support, trying to upend the international order by fashioning a coalition to resist what both countries view as American arrogance.

Whether that is more for show than for real has set off a vigorous debate in Washington, where some government officials and international specialists dismiss the prospect of a more meaningful alliance between Russia and China because of the fundamental differences between the countries. But others said the Obama administration should take the threat seriously as Moscow pursues energy, financing and military deals with Beijing.

“We are more and more interested in the region that is next to us in Asia,” said Sergei I. Kislyak, the Russian ambassador to Washington. “They are good partners to us.” He added that a recent natural gas deal between Moscow and Beijing was a taste of the future. “It’s just the beginning,” he said, “and you will see more and more projects between us and China.”