Following visits to Africa, including to Mali and Algeria, in 1965, at the age of 22, Halevi moved to Israel. He is quoted as having said: "I came to Israel because in Algeria I discovered the importance of the Palestinian problem. I sat there in coffee houses, I heard people, I spoke with intellectuals and I understood that the Palestinian question preoccupies the people of the Arab world. It is really in the center of their obsessions. I decided I want to study this reality up close and from the inside…I wanted to study the Israeli reality." Halevi joined the Palestinian resistance movement and Fatah in particular after the 1967 Arab-Israeli war, and subsequently became a prominent member of the PLO. He was the PLO's representative in Europe and to the Socialist International since 1983, former PLO vice-minister of Foreign Affairs, and participated in that capacity in the Madrid Conference of 1991. He was also a member of the Fatah Revolutionary Council, elected in 2009, and served as an adviser to Yasser Arafat.