The message will be formally delivered to the Pope by President Moon of South Korea when he visits the Vatican this month.
"China and U.S. relations are at an important juncture and facing challenges", Yang said.
Kim Jong-un has invited the Pope to visit North Korea as the dictator arrived for a meeting with a US Secretary of State in a brand new Rolls-Royce. Pope Francis would receive a warm welcome if he visited Pyongyang, Mr Kim was quoted as saying.
State Department spokeswoman Heather Nauert said Pompeo "directly addressed areas where the United States and China do not agree, including on the South China Sea and human rights".
Trump, tweeting from Washington shortly after Pompeo left North Korea, cited progress Pompeo had made on agreements Trump and Kim reached at their June summit in Singapore and said, "I look forward to seeing Chairman Kim again, in the near future".
That makes any focus on a second Trump-Kim summit misguided, Klingner of Heritage said.
South Korea's presidential office said in a statement that Kim told President Moon Jae-in during their summit last month that the pope would be "enthusiastically" welcomed in North Korea.
They also said the two sides agreed to hold a second round of negotiations between the United States and North Korea as early as possible.
DPRK is the acronym for the North's official name, the Democratic People's Republic of Korea.
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Following their meeting a day earlier, Kim was heard saying to the top USA diplomat, "I am really pleased for this opportunity".
Pompeo met Wang and Yang Jiechi, a senior Cabinet official and former foreign minister, after talks Sunday with Kim in North Korea's capital, Pyongyang. Trump said on Twitter that, "Progress made on Singapore Summit Agreements!"
The KCNA said that Kim also expressed "will" and "conviction" to make progress on issues of mutual concern, apparently indicating the denuclearization talks that have nearly been stalled since the June summit in Singapore.
Pompeo said the two sides agreed to have "more frequent and higher-level working group discussions than we've had in some time on a set of issues" and stressed that "ultimately some of these big, hard issues have to be resolved by the nations' most senior leaders, and we're hoping to have those presented in a way that the two leaders can resolve them when they get together".
Pompeo, however, told a reporter traveling with him Monday that "we made significant progress".
Pompeo's visit to Pyongyang marked the fourth of its kind.
The desire to welcome the leader of the Catholic church comes as Kim attempts to transform his image from paranoid head of a rogue state to young and dynamic world leader.