Update: A leaked Department of Homeland Security memo that discussed possible ties between Jared Lee Loughner, the alleged shooter of Rep. Gabrielle Giffords, and hate group American Renaissance, contained errors and overstated the connection, an Arizona law enforcement official told Politico. The new information refutes earlier reports by Fox News on a potential link between the Tucson shooter and the group, based on a law enforcement memo that reportedly included information from DHS. A DHS official told The Washington Post on Monday the agency has not officially provided information on Loughner to any law enforcement officials, but may have done so unofficially.

The commander of the agency that originated the memo said the document "was never intended for public dissemination" and contained incorrect statements. "I do have no reason to believe in anything that we did that (Loughner) had any direct connection or was being directed by American Renaissance," David Denlinger, commander of the Arizona Counter Terrorism Information Center, told Politico.

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WASHINGTON -- Jared Lee Loughner, the alleged shooter of Rep. Gabrielle Giffords and others on Saturday, may have ties to anti-Semitic, anti-immigration hate group American Renaissance, according to a "a law enforcement memo based on information provided by DHS," Fox News reported. A DHS official told the Washington Post on Monday the agency has not officially provided information on Loughner to any law enforcement officials, but may have done so unofficially.

It's unclear whether Loughner maintains a direct connection to the group, however, "strong suspicion is being directed" at American Renaissance in the wake of the group being referenced in Loughner's Myspace and YouTube videos, according to the memo, which was obtained by Fox News.

American Renaissance is a white nationalist group that operates under a pseudo think tank called the New Century Foundation. The group runs a magazine and conferences based on eugenics and the superiority of whites, according to Southern Poverty Law Center.

The group considers its members to be "racial-realists," according to an "About Us" section on the American Renaissance magazine website. "Attempts to gloss over the significance of race or even to deny its reality only make problems worse," the group writes. "Progress requires the study of all aspects of race, whether historical, cultural, or biological. This approach is known as race realism."

The pseudo-science in the magazine refers to biological superiority of whites, with titles such as "Swine Flu: Is There a Racial Link?" and "Ignoring Biological Reality Means Social and Economic Catastrophe." After President Barack Obama was elected in 2008, the magazine ran a feature called "Transition to Black Rule?"

American Renaissance is opposed to the entry of non-whites into the United States and supports Arizona's SB 1070 immigration law, which was criticized as racist and challenged by the Obama Justice Department. In an introduction to readers when the magazine was started in 1990, the publication wrote that "blacks and Hispanics are, compared to whites, far more likely to be poor, illiterate, on welfare, or in jail; they are far more likely to have illegitimate children, be addicted to drugs, or have AIDS. By no definition of international competitiveness can the presence of these populations be anything but a disadvantage."

The group's connection to anti-Semitism is slightly more complicated. Although Holocaust deniers and neo-Nazis are often present at New Century Foundation conferences, group founder Jared Taylor cracked down on anti-Semitic speech in the magazine and at events, according to Southern Poverty Law Center. But after an anti-Semitic outburst at the 2006 conference, the group lost some of its Jewish supporters.

Although the motivations behind Saturday's actions remain unclear, Jewish media organizations pointed to possibly anti-Semitism after Hitler's Mein Kampf was listed as one of Loughner's favorite books. Giffords is the first Jewish U.S. representative to be elected in Arizona. Gabe Zimmerman, a Giffords aide who was killed in the shooting, was also Jewish.

On immigration, Giffords holds Blue Dog views: She supports comprehensive immigration reform, including increased border security and a path to legal status for some of the estimated 11 million undocumented immigrants already in the United States. Giffords voted in December for the DREAM Act, a bill that would allow undocumented immigrants who entered the country as children, to exchange in return for military service or attending college.

Although she opposes Arizona law SB 1070, Giffords also opposed the Justice Department's lawsuit against the state to stop the law. "Congresswoman Giffords wants more federal agents on the Arizona border, not federal lawyers in court arguing with state lawyers about a law that will do nothing to increase public safety in the communities she represents," her spokesman told The Hill in June.

Giffords is mentioned several times on the American Renaissance website, but only in comments and articles from other news outlets on SB 1070 and the 2010 midterm elections.