Chinese Vice President Xi Jinping addresses the opening ceremony of the autumn semester of the Party School of the Communist Party of China in Beijing on Sept. 1. Chinese micro-bloggers and overseas websites have come up with all kinds of creative speculation as to why President-in-waiting Xi has gone unseen for more than a week. (Li Tao/AP/Xinhua News Agency)

China’s president-in-waiting, Xi Jinping, canceled a planned meeting in Beijing on Monday with the visiting Danish prime minister — his third no-show for a meeting with a foreign dignitary this month — fueling speculation that the country’s carefully orchestrated leadership transition had run into more unexpected turbulence.

Chinese government spokesmen offered no explanation for the latest cancellation or why Xi, who is vice president, has not appeared in public since Sept. 1. Last week, Xi canceled a scheduled meeting with Secretary of State Hillary Rodham Clinton and another planned meeting with Singaporean Prime Minister Lee Hsien Loong.

Unconfirmed reports at the time said Xi may have thrown out his back and was recuperating. The cancellation of the Clinton meeting was also seen as a possible snub, to show the Beijing leadership’s pique with the Obama administration’s China policies.

But Monday’s cancellation with Prime Minister Helle Thorning-Schmidt sparked a fresh round of speculation, with possible explanations for Xi’s absence ranging from more serious health concerns to possible instability and intrigue at the very top of the Communist Party hierarchy.

The Chinese government continued Tuesday to duck questions about Xi’s whereabouts. “I have no information on that to provide to you,” said foreign ministry spokesperson Hong Lei when asked about Xi’s health at a regular press briefing in the afternoon.

When asked whether Xi was even still alive, Lei replied tersely, “I hope you will raise serious questions.”

When other reporters tried pressing him on Xi again, Lei shut them down. “I have already answered the question for your colleagues,” he said. “Next question.”

China’s Communists are due to meet later this year to name a new president — widely expected to be Xi — and new members of the now nine-member Politburo Standing Committee that effectively runs the country. But remarkably, as of now, no date has been announced for the conclave. That has added to the sense that the behind-the-scenes jockeying remains intense and that not all is settled among the leadership’s competing factions and personalities as they dole out the top positions.

At the very least, Xi’s disappearance from public view and the unofficial, conflicting accounts of his absence starkly illustrate the challenge facing China’s Communist rulers as they try to stage-manage an anachronistically closed and secretive transition process for the first time in the age of microblogging and social media. Chinese leaders remain opaque and largely loathe even rudimentary forms of transparency — particularly when it comes to their health. But in the absence of real information, the microblogs have swiftly stepped into the void.

“You see the tension, with elite politics not changing as fast as society is changing,” said Cheng Li, an expert on China’s leadership with the Brookings Institution in Washington. Now, he said, “there’s a lack of transparency, so we end up with all these” rumors.

The most oft-repeated speculation, which first surfaced on overseas media sites, was that the portly Xi threw out his back, either while swimming, playing soccer or, according to one version, playing golf.

A more serious version of that rumor is that the vice president had a mild heart attack. Meanwhile, a Chinese-language Web site that often reports on the inner workings of the leadership — and has produced some accurate reports and even more wild misses — said Xi may have been targeted in a car accident by a military associate of deposed Politburo member Bo Xilai, whose wife, Gu Kailai, was recently convicted of murdering a British businessman. That report was later taken down.

Most outside analysts said a health problem, rather than politics, appeared to be the most credible explanation. If China were facing a serious crisis, they said, President Hu Jintao would probably not have traveled out of the country to Vladivostok, Russia, for an Asia-Pacific Economic Cooperation meeting over the weekend.

But they noted that Xi’s problem must be so serious that officials cannot even produce a current photograph of the vice president to stanch the online speculation.

On Monday, a Beijing newspaper did publish a picture of Xi speaking to students at a Communist Party school, but it was from Sept. 1.

“What if it’s a more serious health problem? That’s something you don’t want to publicize,” said Dean Cheng, a China expert with the Heritage Foundation in Washington. Whatever it is, Cheng said, “you have a medical problem with Xi that is interfering with his ability to conduct state business.”

The cryptic and defensive statements from the Foreign Ministry have not helped stem speculation that something is amiss. “We have told everybody everything,” the spokesman, Hong Lei, was quoted as saying Monday.

And as always in times of crisis, China’s leaders have dealt with the Xi disappearance in typical fashion – trying to block Internet users searching for any related terms about the vice president and his possible malady. On Monday, some searches for terms like Xi’s name in English and “back pain” were being blocked from some popular microblogging sites.

Even a relatively mild medical ailment might be cause for China’s leaders to keep Xi’s condition under wraps. This year’s transition is coming at a particularly delicate time, with the Chinese economy slowing dramatically — bringing the risk of social unrest — and fallout continuing from the Bo Xilai case. “In the midst of a transition, any sign of weakness, even physical weakness like throwing out your back, can be seen as a problem,” Cheng said.

“Nature abhors a vacuum, and the Chinese leadership loves creating vacuums,” Cheng said. “With social media, you can get a rumor going, then it will spread like wildfire across the country.”

Jia Lynn Yang contributed to this story from Beijing.