Twice this year, Omar has apologised for tweets that critics said had anti-Semitic overtones, but she has defended her latest comments questioning Israel supporters' "allegiance" - arguing that she is only raising questions about Israeli government policy and US support for it.
In Ocasio-Cortez, the breakout liberal star of the House new class, Omar has a powerful ally who is able to reach a wide audience on social media.
Ocasio-Cortez said Omar "has demonstrated a willingness to listen+work w/impacted communities" and thus should not be subject to a "calling out" from fellow Democrats in the House.
"If House leadership is creating a standard & committing to calling a resolution for every incident . . . then that's a clear way to address the issue & we can all understand," she added. "But if they're not, I think it's valid to ask why not."
A senior Democratic aide noted that Smith quickly apologised for his "go back to Puerto Rico" remark and that the lawmaker targeted, Representative Tony Cárdenas, D, did not pursue official sanctions against Smith.
Ocasio-Cortez's tweets came hours after US President Donald Trump used his Twitter account - with nearly 59 million followers - to lambaste Omar: "Representative Ilhan Omar is again under fire for her terrible comments concerning Israel. Jewish groups have just sent a petition to Speaker Pelosi asking her to remove Omar from Foreign Relations Committee. A dark day for Israel!"
Questioned about the resolution, Senate Majority Leader Mitch McConnell, R, said it was time for the country "to think again about anti-Semitism," and criticised Omar without mentioning her by name.
"It seems to be more fashionable in Europe, it seems to be more fashionable in this country, regretfully, among at least some members of the new class in the House," McConnell told reporters at his weekly news conference. "We need to stand up to it in every way we possibly can."
Amid pressure from Republicans, Democratic leaders are not considering removing Omar from any committee posts, according to three people familiar with the internal discussions among party leaders. But they are mindful of how the increasingly aggressive criticism of Israeli Government policy from Omar, Ocasio-Cortez and other liberals is creating tensions inside the Democratic caucus, where pro-Israel sentiment generally remains strong.
Representative Juan Vargas, D, tweeted that "questioning support for the US-Israel relationship is unacceptable" - prompting Ocasio-Cortez to ask him publicly to "further explain his stance."
"I remember a time when it was 'unacceptable' to question the Iraq War. All of Congress was wrong, including both GOP & Dem Party, and led my generation into a disastrous + wrong war that virtually all would come to regret," she wrote.