The Minnesota representative was involved in a heated exchange on Twitter with Nita Lowey, a fellow Democratic politician, over her recent comments about the influence of pro-Israel groups in Washington.
"I want to talk about the political influence in this country that says it is OK for people to push for allegiance to a foreign country," Ms Omar said, at an event on Wednesday, according to The New York Times.
Her statement was immediately criticised by figures on both sides of the aisle in Congress, for using stereotypes about Jewish people.
"I am saddened that Rep. Omar continues to mischaracterize support for Israel," Ms Lowey said on Twitter.
"I urge her to retract this statement and engage in further dialogue with the Jewish community on why these comments are so hurtful."
Ms Omar defended herself in a series of tweets posted on Sunday night.
"Our democracy is built on debate, Congresswoman! I should not be expected to have allegiance/pledge support to a foreign country in order to serve my country in Congress or serve on committee," she said.
"I have not mischaracterized our relationship with Israel, I have questioned it and that has been clear from my end.
"I am told everyday that I am anti-American if I am not pro-Israel. I find that to be problematic and I am not alone.
"I just happen to be willing to speak up on it and open myself to attacks."
The Democrat's suggestion that pro-Israel politicians "have allegiance" to the Middle Eastern country has attracted a further backlash, with some politicians claiming that Ms Omar is using antisemitic tropes.
"No member of Congress is asked to swear allegiance to another country," Ms Lowey said.
"Throughout history, Jews have been accused of dual loyalty, leading to discrimination and violence, which is why these accusations are so hurtful."
Debbie Wasserman Schultz, another Democratic congresswoman, also attacked Ms Omar's remarks.
"Sadly, misunderstandings over anti-Semitic, hurtful comments continue," the Florida representative said on Twitter.
"Dialogue leads to understanding. @IlhanMN, repeated misunderstandings would seem to require dialogue to avoid repetitive harm.
"Communication is the key to understanding. I hope you agree and will engage so tensions do not worsen."