Achinoam Nini, a singer and peace activist, has long stirred controversy here. Known abroad by her stage name, Noa, she has recorded with Arab artists, refused to perform in the occupied West Bank, condemned Israeli settlements there and had concerts canceled because of bomb threats from the extreme right.

But lately it is the left that has been angry with Ms. Nini. Chosen by Israel to represent the country at the Eurovision Song Contest — this year being held in Moscow in May with an expected television audience of 100 million — Ms. Nini asked if she could bring along her current artistic collaborator, an Israeli Arab singer, Mira Awad.

The selection committee liked the idea of having both Arab and Jewish citizens in the contest for the first time. But coinciding as it did with Israel’s Gaza war and the rise of Avigdor Lieberman, the ultranationalist politician who threatens Israeli Arabs with a loyalty oath, the committee’s choice was labeled by many on the left and in the Arab community as an effort to prettify an ugly situation.

A petition went around demanding that the duo withdraw, saying they were giving the false impression of coexistence in Israel and trying to shield the nation from the criticism it deserved. It added, “Every brick in the wall of this phony image allows the Israeli Army to throw 10 more tons of explosives and more phosphorus bombs.”

Neither Ms. Nini, 39, nor Ms. Awad, 33, has been deterred. But since they consider themselves peace advocates, they are a bit surprised. The antiwar movement, they say, seems to have turned into a Hamas apology force. That, together with the political turn rightward in Israel, means that while the two are being sent to represent this mixed and complex society, they also feel a bit orphaned by it.

“I am so worried by the drift to the extremes on both the Israeli and Palestinian sides,” Ms. Awad said as she and Ms. Nini, and their artistic collaborator, the guitarist Gil Dor, took a break from rehearsal to discuss the controversy. “That is not my vision of a Palestinian state, an extreme religious state where people they don’t like are shot in the legs. And then the Israeli election went to the right.”

The three are preparing four songs, from which one will be selected by a panel and an audience voting at a television performance in early March. All four songs are written in equal parts Hebrew, Arabic and English, and all seek to recognize the difficulty inherent in coexistence, rather than celebrate some mythic Kumbaya.

“And when I cry, I cry for both of us, my pain has no name,” go the lyrics of one of their offerings. “Where can we go from here? Sister, it’s been one long night,” goes a second one. Ms. Awad is one of one and a half million Arab citizens of Israel’s more than seven million inhabitants. There are four million more Palestinian Arabs in the West Bank and Gaza who have no state of their own.

The two women have been collaborating for nearly eight years. At the height of the second intifada six years ago, they did a version of the Beatles’ “We Can Work It Out” that became an international hit.

Ms. Awad, the daughter of an Arab physician from the Galilee and a Bulgarian mother, lives in Tel Aviv. She is best known in Israel as an actress who appears in a popular television comedy, and has been starring lately in a searing play at the Cameri Theater in Tel Aviv about the Israeli-Palestinian conflict.

But it is Ms. Nini who has a true international reputation. She has sold well over a million albums and has a strong following in Europe, especially in Spain, Italy and France, where she gives frequent concerts. She has a crystalline voice joined to a Yemenite Jewish background that give her music a rich ethnic quality. Having spent her childhood in New York City, she speaks flawless English and combines a number of instruments and rhythms to produce music across a broad range of styles.

“I carry a cross-cultural flag, breaking barriers between religions,” she said. “And I am also involved in other things — I am a U.N. good-will ambassador. So I feel like a kind of fusion, like Barack Obama.”

Ms. Nini, while admired in Israel, is more popular abroad. Her music, unlike that of most pop stars, is less a reflection of her own country’s sensibility than an effort to express the universal — one reason the panel may have thought she could bring home Israel’s fourth Eurovision victory in three decades. Israel’s two leading television satire shows have portrayed her as more interested in Italy than Israel, and as exploiting Ms. Awad for her own needs.

Ms. Awad, with her mixed parentage, is also something of a stranger in her own land, an Arab Christian singer and actress in a country dominated by Jews and Muslims.

That partly explains their bond, the two women say, and it may also explain the ambivalence with which their selection has been met.

But recent politics have also clearly taken their toll. During the war, Ms. Nini posted a letter on her blog condemning the Islamists of Hamas and calling on her “Palestinian brothers” to join together to eliminate what she called the ugly monster of Hamas. It was widely interpreted as an endorsement of Israel’s war in Gaza, although she said it was not.

“What I wrote was based on what my Palestinian friends in Gaza told me, that they are threatened by Hamas,” she said.

Both singers and their collaborator, Mr. Dor, say that they spend many hours arguing over the meaning of a Jewish democratic nation, the Israeli-Palestinian conflict and how to do their part to make things better.

“Everyone is responsible to put in his or her two cents for peace and coexistence,” Ms. Nini said. “Our two cents is music. We have a real friendship. Of course we argue. But the beauty is that we offer an example of what coexistence could look like.”