The United States has been concerned for half a decade about when North Korea will succeed in the difficult task of mating a nuclear weapon to an accurate missile — and it has already taken the North more time than American intelligence agencies once estimated.

Almost exactly five years ago this month, Robert M. Gates, then the secretary of defense, on a similar trip to Beijing, warned his Chinese counterparts that he believed the North was within five years of reaching that milestone. To date they have not — it is unclear whether the North Koreans have designed a warhead small enough to fit atop the missile and able to withstand the stresses of atmospheric re-entry — and this week American officials would not say how far they believe the North is from that goal.

In interviews, American officials say Mr. Kerry made the case that the nuclear and missile threat was “a direct threat to the U.S.,” a way of explaining to the Chinese why North Korea’s fourth nuclear test cannot be shrugged off as merely symbolic.

Yet the Chinese have been resisting broad new sanctions against Pyongyang, just as they stripped such sanctions out of a United Nations resolution in 2013, after the North’s last nuclear test. Instead, the officials say, Beijing is pressing for targeted sanctions against individuals in the North Korean nuclear complex, which are unlikely to have serious repercussions.

Mr. Kerry adopted the tough tone after nearly five hours of talks with Mr. Wang that were dominated by North Korea and what the United States and China, a treaty ally of the North, should do in the aftermath of the latest nuclear test. Mr. Kerry was referring to the deployment of a missile defense system to South Korea that has been under discussion for some time but that the South, an American ally, has resisted because of China’s opposition. The system is called Terminal High Altitude Area Defense, or Thaad; China views it as a threat to its own capabilities in the Pacific.