BEIJING — Slowing economic growth. A ra n corous trade war. Recalcitrant protesters in Hong Kong. A mass die-off of pigs and surging food prices. The frustrations are piling up for China’s lea der, Xi Jinping.

But a gathering of the Communist Party elite this week will grapple with lurking risks that worry him more: dysfunction, divisions and disloyalty in the party.

Communist Party rule could eventually crumble if the party fails to constantly reinforce its grip on China, Mr. Xi said in a recently published speech, citing ancient emperors whose dynasties rotted from corruption, lax discipline and infighting. The Central Committee, a party conclave of about 370 senior officials, began meeting in Beijing for four days on Monday to approve policies intended to ward off such dangers.

“From ancient times to the present, whenever great powers have collapsed or decayed, a common cause has been the loss of central authority,” Mr. Xi said in the speech, which was given early last year but not issued till this month in a leading party journal, Qiushi.