BEIJING — President Trump has often said he is counting on Xi Jinping to do the right thing with North Korea, alternately praising and prodding the Chinese leader about enforcing tougher sanctions, and even holding off on his campaign promises to get tough on trade in the hope Mr. Xi follows through.

To his frustration, however, Mr. Xi has proved adept at taking incremental steps while always stopping short of the more punishing measures that the White House believes would truly threaten the North Korean regime and force it to scrap its nuclear arsenal.

The pattern is a familiar one. Other American presidents turned to China to solve the North Korea problem too, and were generally disappointed. But with the North closing in on a nuclear missile that can hit the United States, there has never been more riding on this strategy.

Mr. Trump arrived in China on Wednesday for the stiffest test yet of his audacious bet: that by cultivating Mr. Xi and offering him concessions, like delaying punitive trade moves, he can persuade him to move against North Korea in a way that none of his predecessors have.