Jen Psaki bluntly told the White Press corps that she would not discuss the QAnon supporting congresswoman in her briefings moving forward.
Ms Psaki was asked if the president had any response to disciplinary action that the freshman Representative should face for her comments.
“We don’t, and I am not going to speak further about her, I think, in this briefing room,” said Ms Psaki.
Republican House leader Kevin McCarthy says he plans to speak to Ms Taylor Green about the “deeply disturbing” comments.
In 2019 Mr McCarthy stripped former congressman Steve King of his committee privileges over his comments on white supremacy, effectively ending his career as he lost his primary in Iowa over his lack of influence.
Ms Taylor Greene reportedly posted a string of far-right conspiracy theories to her Facebook account, according to CNN.
In one, from January 2019, Ms Taylor Greene liked a comment that said “a bullet to the head would be quicker” to remove House Speaker Nancy Pelosi, a Democrat from California.
She also liked other posts that talked about executing FBI agents, who she regarded as part of the “Deep State” working against Donald Trump.
In an April 2018 Facebook post the lawmaker wrote about Barack Obama’s Iran deal, with a commenter asking her, “Now do we get to hang them? Meaning H &O???,” in an apparent reference to Mr Obama and Hillary Clinton.
“Stage is being set. Players are being put in place. We must be patient. This must be done perfectly or liberal judges would let them off,” she replied.
Ms Taylor Greene took to Twitter to defend herself.
‘“Over the years, I’ve had teams of people manage my pages. Many posts have been liked. Many posts have been shared. Some did not represent my views,” she wrote.
Ms Taylor Greene last week, as a stunt, filed an article of impeachment against Joe Biden the day after his inauguration.
She also had her Twitter account suspended by the social media giant for 12 hours for violating its rules following the 6 January Capitol riot.
Ms Taylor Greene has also been accused of posting false flag conspiracy theories about the Parkland high school shooting.
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