The historic dialogue between a Washington rabbi and the leader of the group once known as Black Muslims advanced another step last month when Rabbi Joshua O. Haberman stepped before an ornately carved pulpit in Chicago to address a cheering crowd of Muslims.

The appearance of Haberman at Masjid Elijah Muhammad was on response to an invitation form Wallace Deen Muhammad, who has become the chief man, or spiritual leader, of what is now known as the World Community of Islam in the West.

Five months earlier, Muhammad had been Haberman's guest, in an unprecedented address at the Friday night services of the Washington Hebrew Congregation. Last month, it was the Muslim leader's turn to open his pulpit to the rabbi.

"It was truly incredible experience." Haberman said of his appearance before the crowd of 2,000 Chicago Muslims seated, shoeless, the men in front and the women in the rear, on the carpeted floor of their mosque, which had been converted from a Greek Orthodox Church.

Characterizing the Muslim worshipers as "disciplined, and with an atmosphere of devotion." Haberman said he was "stunned" by his reception.

After his introduction by Muhammad, he began his remarks, he recalled, "and within two or three sentences, the people roared their applause."

The Washington rabbi was full of praise for Muhammad, who took over leadership of the controversial black Muslim organization after the death of his father three years ago and who has sharply reversed his father's anti-white stance.

"Wallace Muhammad has had a difficult job in turning around the movement from the extremism of the past," the rabbi said.

Within recent months there have been serious challenges to Muhammad's leadership and some members have left the movement. But Haberman said he believed Muhammad has "been able to overcome the dissension."

The rabbi said that when he praised Muhammad's substituting racial inclusiveness for his father's extremist policies, the worshipers at the mosque "roared their approvel."

The Bilalian News, the newspaper of the WCIW, devoted a full page to a generally laudatory report and photos of Haberman's appearance at the Chicago mosque.

Haberman said he intends to pursue the dialogue that was begun five months ago in Washington and carried further last month in Chicago. He hopes that continred encounters might bear fruit, both in improving relationships between black Americans and the Jewish community and, just possibly, have a moderating effect on the age-old Arab-Jewish enmity.

"The political approach to problems is not enough," he said. "All the political programs-the New Deal and the New Frontier and Great Society would be fruitless without moral motivation," he said. He praised the WCIW as being "most committed to the religious approach."

He also expressed hope that there could be a "moderating influence of the World Community of Islam in the West on relations between Arabs and Israelis."

That could be particularly important in this country since, he predicted, "there may be millions of Muslims settling in the United States in the years to come."

Haberman, who last year also invited Dr. Muhammad Rauf, director of the Islamic Center here, to address the Washington Hebrew Congregation, says that within the coming year he plans for increased "cultural and religious interchange between the growing Muslin community and the Jewish community."

He said that out of many letters and phone calls commenting on Wallace Muhammad's appearance last winter, there was "only one somewhat negative note from a person who raised serious doubts as to whether the professed expressions of friendship were sincere. The others were all positive...even Christian leaders took time out to express their appreciation of what we were doing."

Haberman recalled that when he stepped, shoeless in deference to Moslem tradition, into the Chicago pulpit. "The first thing I saw was the plaque that said it was a gift of Muhammad Ali."

Musing over the dramatic events, the German-born rabbi observed: "Aside from the theatries, it says to me that you can take international hostilities and within the magic of the American atmosphere, turn confrontation into brotherhood."