It is not just the United States that wants the denuclearization of the Korean Peninsula, but the world, State Department spokeswoman Heather Nauert said Monday.

"Our issue is not with the people of North Korea," Nauert told Fox News' "Fox & Friends," while visiting the program she had hosted in the past as a Fox News correspondent.

"Our issue is with Kim Jong Un. It is not just the United States frankly. It is virtually every country around the world, a chorus of condemnation."

"Allies everywhere" are condemning the actions of North Korea, she said, including this weekend's news the nation had tested a hydrogen bomb, but the push will continue for diplomacy.

"We continue to push forward with this plan for diplomacy because you can't give that up," Nauert said. "That is always the preferred approach, to try to get them to come to the table. We pushed forward with that approach and pushed to try to remove the money that goes into North Korea that helps fund its illegal nuclear and ballistic weapons programs."

Nauert said she has sat in on many meetings between Secretary of State Rex Tillerson and his counterparts around the world, and he has told them he wants them to cut back on North Korean workers in their countries.

"Cut back on mission size, embassy size in your nation," Nauert said Tillerson has said. "Doing those things all across the world helps remove money, hold on from the Kim Jong Un regime. He uses money to fund these very expensive programs. We will continue to push forward with that."