During a House Foreign Affairs Committee hearing Ms Omar brought up Mr Abrams role in the Iran-Contra scandal, in which the US secretly sold weapons to Iran and funnelled the proceeds to Nicaraguan anti-Communist groups.
She also questioned Mr Abrams comments on US policy in El Salvador, including when he seemingly downplayed a massacre in the town of El Mozote in 1981.
"Watching her question Trump's envoy... feels like justice," Ms Ocasio-Cortez wrote.
Mr Abrams called the exchange "ridiculous" and said he would not respond to a "personal attack".
"I don't think this entire line of questioning is meant to be real questions and so I will not reply," he said during the hearing.
What do critics say?
But for all her fans, Ms Omar has not had the easiest start in Washington DC.
She was embroiled in controversy over tweets which some have claimed are anti-Semitic.
A 2012 post of hers resurfaced in which she claimed Israel had "hypnotised the world", provoking outrage for what many saw as an offensive characterisation of Jewish people.
The controversy deepened when she attacked the American Israel Public Affairs Committee (AIPAC), claiming the lobby group is paying politicians to vote for pro-Israel policies.
Republicans and Democrats condemned her comments. House Speaker Nancy Pelosi attacked Ms Omar's "prejudicial accusations" and demanded an immediate apology.
She later did so, tweeting a statement saying she had colleagues "educating me on the painful history of anti-Semitic tropes".
President Trump later called on her to resign from Congress and "certainly" from the House Foreign Affairs Committee, calling the congresswoman "terrible".
Ms Omar fired back with a tweet, writing: "You have trafficked in hate your whole life".
"I learned from people impacted by my words. When will you?"
Ms Omar, like her colleague Ms Tlaib, has also previously expressed support for the pro-Palestinian Boycott, Divestment and Sanctions (BDS) movement, which urges a complete boycott of Israel over its policies towards the Palestinians.
Israel says BDS opposes Israel's very existence and is motivated by anti-Semitism.
"What she did in calling out AIPAC is an important thing," he told the BBC, saying it is "almost forbidden" to say anything critical of Israel in US politics and that Ms Omar was exercising her right to criticise a powerful lobby group.
"We have to be able to distinguish between real anti-Semitism and criticism of Israel," he said. "Her critics are blowing this way out of proportion."
And the campaign finance claims?
Ms Omar's time in state government was not without controversy either.
Minnesota Representative Steve Drazkowski alleges Ms Omar used campaign funds in her local election run to pay her personal lawyer, as well as to take multiple trips around the US and one trip abroad to Estonia which were unrelated to her election campaign.
"She just doesn't respect the law," Mr Drazkowski told the BBC.
The Republican lawmaker says both complaints are now under full investigation by Minnesota's Campaign Finance Board, although a spokesperson for the board told the BBC it does not confirm or deny any complaints or investigations.
Her campaign at the time said Mr Drazkowski's allegations are politically motivated and told the Associated Press that "it should be concerning to his constituents that he is using taxpayer dollars to harass a Muslim candidate".