It came after a resolution calling on the Republican to be stripped of committee assignments was introduced on Tuesday, and could be voted on by Wednesday.
Arguing against her expulsion from congressional committees and Congress altogether, Ms Greene said she had raised more than £100,000 (£73,000) after calling on supporters to “StandWithMTG”.
The pitch, which came as House Republicans planned a retaliation to remove Ms Omar from committee assignments - with the Democrat's picture as a background.
“Help me defend my seat from the DC Swamp,” Ms Greene wrote, with a pitch that included Ms Omar’s picture and the words: “Democrats are trying to expel me from Congress”.
Ms Omar wrote on Tuesday night that the use of her face in the fundraising pitch was “subtle”, after Yahoo News’s national correspondent, Alexander Nazaryan, said it was “unclear” why Ms Greene had targeted the Democrat.
“Unclear why Rep. Taylor Greene is using an image of Ilhan [Omar] in this pitch,” tweeted the reporter, “Since Rep. Omar is not part of Democratic leadership in the House and would have no real say in disciplinary matters.”
Although Ms Omar was among those who called on Ms Greene to be removed amid reports she pushed conspiracies on social media in the past, amid other controversial remarks, she does not have responsibility for Ms Greene’s removal.
The Republican was also widely condemned after rejecting November’s presidential results when Congress voted on 6 January - hours after the Capitol was besieged by the former president’s supporters, many of whom also believed QAnon.
House Republicans - who plan on adding an amendment to the resolution against Ms Greene - argued that Ms Omar should be stripped of committee assignments "in light of conduct she has exhibited," reported Fox News.
Ms Omar wrote before her remarks on Ms Greene’s tweet that “the Radical Right is rooted in misogyny, Islamophobia and racism,” and added: “Stop whitewashing the actions of the bigoted conspiracy theorists, violent insurrectionists and fascist cult followers of Trump. Do better.”
Kevin McCarthy, the Republican House leader, has been given until Wednesday by House Democratic Majority Leader Steny Hoyer to remove Ms Greene’s committee assignments, after he met with the congresswoman on Tuesday.
Democratic congresswoman Jimmy Gomez, meanwhile, said on Tuesday he had 68 co-sponsors to a resolution that would call on Ms Greene to be removed from Congress outright - although it would unlikely to pass the House.
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