DES MOINES — GOP presidential hopeful Scott Walker said Monday that children of illegal immigrants who are born in the United States should not automatically receive U.S. citizenship.

Walker's comments came as he walked through the Iowa State Fair with a swarm of reporters who fired questions at him. A number of the questions focused on immigration, given a controversial immigration plan that GOP frontrunner Donald Trump released over the weekend. That included this question from Kasie Hunt of MSNBC: "Do you think that birthright citizenship should be ended?"

Walker, who is governor of Wisconsin, had been repeatedly asked that question earlier in the day, but this time he responded: "Well, like I said, Harry Reid said it’s not right for this country. I think that’s something we should — yeah, absolutely, going forward." In the early 1990s, Sen. Harry Reid (D-Nev.) introduced legislation that would have clarified the 14th Amendment of the Constitution and revoked birthright citizenship, a position that the Senate Democratic leader has since abandoned.

Hunt asked him again whether the U.S. should end birthright citizenship, and Walker nodded and responded: "Yeah, to me it’s about enforcing the laws in this country. And I’ve been very clear, I think you enforce the laws, and I think it’s important to send a message that we're going to enforce the laws, no matter how people come here we're going to enforce the laws in this country."

Hunt then asked Walker whether  the U.S. should deport the U.S.-born children of illegal immigrants, at which point Walker said: "I didn’t say that — I said you have to enforce the law, which to me is focusing on e-verify," a system by which employers can check the citizenship status of potential employees.

Asked the same question about birthright citizenship later in the day, Walker reverted to his usual talking points on immigration. When asked whether he believes any person born on U.S. soil should be considered a U.S. citizen, Walker responded: "Well, again, I think before we start talking about anything else beyond securing the border, enforcing the laws and having a legal immigration system that gives priority to American working families. Americans aren't going to trust politicians that talk about other things until they feel confident that they're going to do those things."

Wisconsin Gov. Scott Walker, a candidate for the 2016 Republican presidential nomination, spoke at the Des Moines Register Soapbox at the Iowa State Fair. (C-SPAN)

Kirsten Kukowski, a spokeswoman for Walker, followed up in an e-mail and provided this as the governor's position: "We have to enforce the laws, keep people from coming here illegally, enforce e-verify to stop the jobs magnet and by addressing the root problems we will end the birthright citizenship problem." She would not elaborate on what the governor meant in his comments to Hunt.

Immigration has been a tricky topic for Walker, whose northern Midwestern state does not face the same immigration issues as states that share a border with Mexico. Years ago, Walker said he supported granting amnesty to the millions of illegal immigrants already in the U.S., a position that he abandoned this year. Walker has staked out stances that are more conservative than those of most other GOP presidential contenders, including backing the idea of further limiting legal immigration to protect American jobs. Ending birthright citizenship would put him at the far right of the field.

Walker has long said that the U.S. needs to secure its southern border — but on Monday he provided much more detail and said that he supports constructing a wall on the border, an idea made popular by Trump.

"It's a combination of infrastructure — the wall itself — but you also need to have technology and personnel as a part of that," Walker said. He then described the border fence that he saw when visiting Israel this spring: "It's not just having a fence, because if you just have a fence that doesn't have personnel manning it, you don't have the technology to make sure that the fence is secure — that people aren't over it or under it — then you've just built something that's ineffective."