The dispute creates a problem for Pelosi who is trying to maintain unity among Democrats, including Omar and other high-profile new members, as veteran lawmakers who are demanding a clear resolution denouncing Omar's remarks.
Omar's name doesn't appear in the current draft of the resolution, which could go to the House floor as soon as tomorrow, but it denounces anti-Semitism by describing tropes similar to some of those she has invoked.
Omar, 36, apologised for previous comments derided as anti-Semitic, pledging to "combat hate of all kinds," and she has defended her right to question US foreign policy.
Reworking the language of the resolution to be a broader condemnation of prejudice so far has done little to calm her supporters among progressives, including Alexandria Ocasio-Cortez of New York, who said there are far worse examples of offensive behaviour and statements in Congress.
In some cases Omar's supporters defended her underlying point that historic ties between the US and Israel should be reexamined.
Pelosi said she met personally with Omar regarding her comments and said she still hasn't seen the text of the resolution, which is being led by the office of Florida Democrat Ted Deutch. Asked whether she still plans a vote on the measure this week, Pelosi said, "I'm hoping so - when we are ready."
Representative Elliot Engel, chairman of the Foreign Affairs Committee on which Omar sits, said there is no discussion of removing her from the committee, as some Republicans have demanded.
Engel of New York, one of the first Democrats to publicly condemn her comments last week referring to an expectation of allegiance to Israel, said he took personal offence to her words and that an official rebuke is "the right thing to do".
"I don't want to do anything to jeopardise the talks going on right now and wording being worked out, and I don't really want to throw a monkey wrench into it," said Engel, who is Jewish. "But I want to tell you we have to have a strong statement condemning anti-Semitism and I believe we will."
Ocasio-Cortez, a 29-year-old with an outsized social media presence, called the resolution a "nuclear option" on Twitter and urged Democratic leaders to use the moment for a lesson in inclusion, rather than censure.
"I believe that Ilhan, in her statement a few weeks ago, has demonstrated a willingness to listen+work w/impacted communities," Ocasio-Cortez said in a tweet. "If we called resolutions on sexist statements, a good chunk of Congress would be gone. To jump to the nuclear option every time leaves no room for corrective action."
Ocasio-Cortez and Omar, together with Ayanna Pressley of Massachusetts and Rashida Tlaib of Michigan, have called themselves a "squad" in social media posts and have publicly come to each other's defence.
Tlaib, who was on stage with Omar at an event last week when she made the comment about "allegiance to a foreign country" that's been criticised, later compared Omar to "civil rights icons before us who spoke out about oppressive policies."
The resolution would be the second anti-Semitism measure to pass under the Democratic majority, although the first one was presented by Republicans in a surprise procedural vote on a resolution regarding Yemen - the same week Omar tweeted rap lyrics to suggest pro-Israel politicians were motivated by money. Omar apologised for those tweets, but defended her original question about the influence of the American Israel Public Affairs Committee.
Republicans have also been accused of trafficking in anti-Semitic tropes. Jim Jordan of Ohio, the ranking Republican on the House Oversight Committee, on Monday tweeted that the Democratic chairman of that committee, Jerrold Nadler, who is Jewish, was siding with billionaire and impeachment-advocate Tom Steyer, whose father is Jewish.
His spelling of "$teyer" was criticised for suggesting a connection between Jewish individuals and money. Nadler later tweeted that Jordan's comment "counts as both inane AND anti-Semitic."
Omar herself has been the target of prejudice and threats of violence.
Last week, a display from West Virginia Republicans linked Omar, who is Muslim and wears a hijab, to the September 11 terror attacks.
She has received death threats, and she says her experience coming to the US from a refugee camp in Kenya has helped her understand persecution and weather her current controversy.
"I know what it feels to be someone who is of faith that is vilified," Omar said in the same comments that inspired this resolution. "I know what it means to be someone whose ethnicity is vilified."
- Bloomberg