The demands for ideological conformity show that Mr. Xi and other leaders want to inoculate the public from expectations of major political liberalization, even as they explore loosening some state controls over the economy, several analysts said.

“If anything, there seems to be some regression in the ideological sphere,” said Chen Ziming, a prominent political commentator in Beijing who supports democratic change. “I think that there will be some steps forward in economic reform, but there are no notions of political reform. Such warnings reflect that mentality.”

Calls for orthodoxy from Chinese leaders are by no means new. But Mr. Xi is caught in a sharpening conundrum, trying to satisfy widespread public expectations for cleaner, more accountable government and a fairer share of prosperity while also defending centralized control, said Minxin Pei, a professor at Claremont McKenna College in California who specializes in Chinese politics.

“I think in his mind he has two conflicting priorities,” Professor Pei said.

“The top priority is to maintain the party’s rule,” he said. “But he also has this immediate political priority; that is, he wants to show he will end this period of stagnation. But clearly the two priorities are in conflict with each other.”

Mr. Xi has commissioned officials and researchers to study seven areas of potential economic change, including loosening state controls on bank interest rates and on resource prices, said a Chinese businessman with close links to senior leaders, confirming a report in The Sydney Morning Herald on Monday.

Some of the proposals are likely to be endorsed by a meeting of the party’s Central Committee late this year, said the businessman, who spoke on the condition of anonymity, citing concern about harming his ties to leaders.