Last week, Mr. Xi canceled meetings with Secretary of State Hillary Rodham Clinton and the prime minister of Singapore, Lee Hsien Loong. On Monday, he did not show up at a meeting with the Danish prime minister.

While Chinese leaders often do not appear in public for long periods, canceling meetings with foreign dignitaries at the last minute is unusual. Adding to the uncertainty is the absence of an official statement of any kind, with observers talking about a bad back or even a mild heart attack.

“There’s every sort of crazy rumor about Xi’s health,” said a senior Chinese journalist, who asked not to be identified because of sensitivity surrounding the case. “But no one is saying anything.”

The speculation adds another wrinkle to the less-than-smooth transition from the departing president, Hu Jintao, to Mr. Xi. Earlier this year, a senior Communist leader, Bo Xilai, vanished from view after his wife was charged with murdering a British businessman. Then, earlier this month, another senior official was unexpectedly demoted after a scandal surrounding his son.

And no date has been set for the 18th Party Congress, when the transition is supposed to take place. The consensus is that it will happen next month, but no announcement has been made. The last congress was also held in October, but its dates had been made public in August.

“These are not signs that everything is going well,” said Bo Zhiyue, a political-science professor at the National University of Singapore.

China’s political system has long been a black box, but its secrecy has begun to seem more anachronistic as the country has become one of the world’s biggest economic, political and military powers.

“Authorities are worried about anything that may tarnish the transition,” said Joseph Y. S. Cheng, a political-science professor at Hong Kong’s City University. “But this concern is working against their interests; they should come out with a clear statement.”

Some of the rumors have it that Mr. Xi hurt his back swimming or playing soccer; these were given credence by reports from foreign diplomats who say they were told that his bad back had caused him to cancel the meetings with Mrs. Clinton and Mr. Lee.

Less reliable was a rumor that he was hurt in an auto accident when a military official associated with Mr. Bo tried to injure or kill Mr. Xi as part of a revenge plot; the report was later retracted.

One well-connected political analyst in Beijing said he was told by party officials that the rumors of skulduggery were wrong. But he said he was told that Mr. Xi, 59, had suffered a mild heart attack.

“They say it won’t affect the party meeting,” the analyst said.

On Monday, the situation grew odder. China’s Ministry of Foreign Affairs denied that the meeting between Mr. Xi and the Danish prime minister, Helle Thorning-Schmidt, had been scheduled. Last week, however, the ministry had invited the foreign press for a photo opportunity with the two leaders.

“We have told everybody everything,” Foreign Ministry spokesman Hong Lei said, according to The Associated Press.

Adding to the conspiracy theories, on Monday a popular microblogging site, Sina Weibo, banned searches for the term “back injury.”

Almost as if to assuage worries about Mr. Xi’s health, a newspaper on Monday ran a picture of Mr. Xi addressing students at opening of the fall semester of the Central Party School. The photo and speech, however, were from Sept. 1.

—Jonathan Ansfield contributed reporting. Patrick Zuo contributed research.