In another email sent in July 2015, Mr. Miller praised the work of Jason Richwine, an anti-immigration author whose work appears often on the think tank’s website. Mr. Richwine, who has drawn public furor for arguing that Hispanic immigrants are less intelligent than white Americans, said in an email on Thursday that he was a “mainstream” analyst whose work has appeared in The Wall Street Journal and Politico.

“Those publications are not embarrassed to promote my work,” wrote Mr. Richwine, who said that he did not personally know Mr. Miller. “So I don’t know why Stephen Miller should be either.”

In several cases, the think tank has shared with readers links to websites tied to white nationalists, including the site VDARE, which regularly publishes white nationalists and traffics in anti-immigrant messages. Katie McHugh, a former Breitbart editor who leaked the cache of emails, said Mr. Miller emailed her a link to an article on VDARE. Ms. McHugh has said she now denounces far-right groups.

The White House defended Mr. Miller on Thursday by equating the law center’s reporting to libel.

The law center “libels, slanders and defames conservatives for a living and in fact is a discredited, debunked far-left smear organization that has even recently been forced to pay someone $4 million for defamation,” Hogan Gidley, a White House spokesman, said in an email. Mr. Gidley was apparently referring to $3.4 million the group paid to settle a lawsuit filed by Maajid Nawaz, an activist whose advocacy organization the law center initially said was an “extremist” group.

Mr. Gidley also claimed that criticism of Mr. Miller was connected to his Jewish faith. “I work with Stephen,” Mr. Gidley said. “I know Stephen. He loves this country and hates bigotry in all forms — and it concerns me as to why so many on the left consistently attack Jewish members of this administration.”