Washington (CNN) Freshman Democratic Rep. Ilhan Omar of Minnesota is defending her controversial views on Israel as they come under scrutiny in Washington, telling CNN that "it's not surprising" her positions are generating attention and that she finds it "exciting" to be sparking debate.

"It's not surprising. I think it is actually exciting because we are finally able to have conversations that we weren't really willing to," Omar told CNN on Tuesday. "It is really important for us to get a different lens about what peace in that region could look like and the kind of difficult conversations we need to have about allies."

Omar along with Democratic Rep. Rashida Tlaib of Michigan, the first two Muslim women to serve in Congress, are indeed changing the conversation on Capitol Hill over the United States' long-standing relationship with Israel by speaking out critically against the Israeli government over its treatment of Palestinians.

As they challenge the political status quo over Israel in Washington, Omar and Tlaib are facing intense scrutiny and criticism, in particular from Republicans eager to exploit divisions in the Democratic Party.

Tlaib and Omar have also broken the mold on Capitol Hill by supporting the Boycott, Divestment and Sanctions movement. The movement is a non-violent activist campaign that aims to put economic and political pressure on Israel over its actions toward Palestinians, including calling for an end to Israeli occupation of the West Bank.

Omar told CNN that Israel should be held accountable for living up to "the same values that we push for" in the United States as one of its allies.

"Israel is an ally of the United States and I think as much as you would look to your neighbor to your friends to live out the same values as you are, we want to make sure that our allies are living out the same values that we push for here," she said.

Republicans react critically

In her first month in Congress, Republicans have been quick to criticize Omar, a Somali immigrant who came to the US as a refugee more than two decades ago, for statements she has made regarding Israel.

Rep. Lee Zeldin, a Republican from New York, pointed out in a tweet last month that Omar supports the BDS movement and in 2012 made a statement saying that "Israel has hypnotized the world, may Allah awaken the people and help them see the evil doings of Israel." Highlighting that statement, Zeldin argued that rather than supporting Israel and countering anti-Semitism, Democrats "are now empowering it."

The 2012 statement from Omar came in the midst of an eight-day war between Israel and Hamas. Israel said it had to counter attack because of consistent rocket fire from Gaza into civilian areas of Israel.

The Israel Defense Forces said Israel launched at least 1,500 airstrikes on Gaza. The Gaza Ministry of Health said 163 Palestinians were killed and more than 1,000 wounded. Hamas' military wing, the al Qassam brigade, said it fired 1,573 rockets toward Israel during the hostilities. Six Israelis were killed, and at least 200 wounded.

Omar has since expressed regret for her choice of words, saying that she had "unknowingly" used an "anti-Semitic trope" and that her statement "came in the context of the Gaza War."

Zeldin also posted an anti-Semitic voicemail he received to Twitter last month and tagged Omar, asking the congresswoman, "Would love to know what part of this hate filled, anti-Semitic rant you disagree with? I disagree with all of it. Do you?"

Omar responded by saying, "This is heinous and hateful. I too am flooded with bigoted voicemails and calls every day. Maybe we could meet and share notes on how to fight religious discrimination of all kinds?"

In an interview with Yahoo News , Omar was asked how the US can work toward peace between Israelis and Palestinians and answered that "an equal approach to dealing with both" is necessary.

She elaborated on that by saying, "Most of the things that have always been aggravating to me is that we have had a policy that makes one superior to the other."

"When I see Israel institute law that recognizes it as a Jewish state and does not recognize the other religions that are living in it and we still uphold it as a democracy in the Middle East, I almost chuckle because I know that if we see that in any other society we would criticize it, we would call it out -- we do that to Iran, we do that to any other place that sort of upholds its religion."

Omar appears to have been referencing Israel passing into law last year a controversial bill that declares that the Jewish people have an exclusive right to national self-determination in Israel.

Prime Minister Benjamin Netanyahu, who had advocated for the nation-state bill, hailed its passage and called it a "defining moment" in Israel's history, but critics, including some strong supporters of Israel, expressed concern that it would weaken and undermine Israeli democracy.

The National Republican Congressional Committee highlighted Omar's remarks to Yahoo News by saying on its website that the congresswoman's "latest anti-Semitic attack included comparing Israel to Iran."

Omar and Tlaib argue they're not attacking a faith

Both Omar and Tlaib have made a point to argue that their criticism of actions by the Israeli government should not be viewed as an attack on a faith.

"When I talk about places like Saudi Arabia or Israel or even now with Venezuela, I'm not criticizing the people. I'm not criticizing their faith, I'm not criticizing their way of life," Omar said in a recent appearance on Comedy Central's "The Daily Show with Trevor Noah."

"What I'm criticizing is what's happening at the moment, and I want for there to be accountability so that the government, that administration, that regime can do better," she said.

Tlaib, who is the first Palestinian-American woman to serve in Congress, explained her support for the BDS movement by invoking freedom of speech in an interview with CNN prior to her swearing in -- and made a point to say that the movement is not an attack on a faith.

"I don't like the criminalization of freedom of speech and so much of my principles around BDS to me are -- I know for so many it might trigger these other thoughts about it, for me though, it is very much tied to core values around freedom of expression and freedom of speech. So to be able to do economic boycotts is connected," she said.

She added, "for those that think this is some sort of attack on a faith, I just want to push back and say no this is really about racism, about inequality and about human rights."

House Republican leader Kevin McCarthy was asked at a news conference Friday about GOP criticism of Tlaib and Omar over their comments on Israel and whether he believes it's possible to be critical of the Israeli government and its policies without being anti-Semitic.

"It's possible," McCarthy responded, "but I think the language they are using is wrong," though he did not point to any specific examples.

Speaking at a Center for American Progress event on Tuesday, Omar said that people should be able to practice all religions freely.

"I know how it feels to be hated because of my religious beliefs. I am proof that as Americans we can embrace our differences," she said.

Omar added, "The core of Islam, just like Christianity and Judaism, is the radical message of human equality in the eyes of God. We also must recognize that religious hate of all kind, whether it is against Muslims, Jews, Christians or atheists, are linked."

Omar's office initially declined an interview, but CNN was able to speak with her as she was leaving the event. Omar did not respond to questions, however, about why she supports the BDS movement. Tlaib declined to answer questions from CNN in the halls of the Capitol on Wednesday.

Tlaib hopes to lead congressional delegation to the West Bank

Polling does show shifting sentiment among Democrats in their views of Israel and Palestinians. A Pew poll last year found that support for Israel among Democrats and independents has fallen and support has risen among Republicans and that Democrats are divided over which side in the conflict they sympathize more with.

Tlaib, however, has faced public push back from within the ranks of House Democrats for saying that she plans to lead a congressional delegation to the West Bank, where her grandmother still lives. Member of Congress regularly take congressional delegation trips to Israel.

Democratic chairman of the House Foreign Affairs Committee Eliot Engel of New York told the Al-Monitor that "instead of her talking about things, she's new here, she ought to listen and learn and open her mind and then come to some conclusions," in reference to the idea of a West Bank delegation.

The next day, Tlaib tagged Engel in a tweet, saying, "how are we ever going to obtain peace? I hope you'll come with me on the trip to listen and learn. My sity (grandmother) will welcome you with an embrace & love. Please feel free to call me if you have anything to say. I am your colleague now."

Tlaib told CNN in the interview prior to her swearing in that she believes "we'll get closer to peace" when "we start addressing the humanitarian needs of both Israelis and Palestinians ... when we're not thinking the other person is less than or less deserving."

Tlaib faces scrutiny over a photograph

Tlaib has also faced controversy after a man named Abbas Hamideh posted a photo with her to Twitter last month with the caption, "I was honored to be at Congresswoman @RashidaTlaib swearing in ceremony in #Detroit and private dinner afterward with the entire family, friends and activists across the country."

Jonathan Greenblatt, the CEO and national director of the Anti-Defamation League, drew attention to the photograph several days later on Twitter , saying that Hamideh has "equated Zionists with Nazis" and calling on Tlaib to "denounce his anti-Semitism." The ADL is also critical of the BDS movement and argues on its website that the movement "is the most prominent effort to undermine Israel's existence."

In late January, Zeldin introduced a House resolution that calls for a rejection of anti-Israel and anti-Semitic hatred in the US and around the world. The text of the resolution mentions Tlaib and Omar by name, citing, among other things, the controversy over Hamideh as well as Omar's statement that "Israel has hypnotized the world."

Asked for comment on the photo, Tlaib told CNN through a spokesman, "I oppose hate and violence in all forms and will continue to work for peace. It is also important to note, I've taken thousands of photos over the course of my campaign and now during my tenure. A photo does not mean I agree with anything someone says. It is obvious this man thrives on media attention from his recent posts. It's unfortunate that he was successful. I do not agree with the statements brought to my attention."

The congresswoman also recently gave a lengthy statement to The New York Times in which she said, "It is unfair to be held responsible for the statements of others, especially when my actions ... make clear that I oppose all forms of hate and condemn those who dehumanize others."

She added, "It is disappointing that some of my colleagues are feeding into the hate and division and mislabeling me to ignite fear."