Gruenbaum was known for his courageous and militant stance against his opponents and on behalf of minorities' interests, while equally critical of the ultra-orthodox party Agudat Israel and Jewish lobbying.

After moving to Paris in 1932, Gruenbaum immigrated to Mandatory Palestine in 1933 after being elected to the Jewish Agency Executive (the board of directors), during the Eighteenth Congress[1] of the Zionist Organization.

During the Holocaust, he served on the "Committee of Four" chosen at the outbreak of World War II to maintain contact with Polish Jewry and aid in their rescue.

In 1942, when word reached the Yishuv of the mass extermination by the German occupying forces taking place in Eastern Europe, Gruenbaum was chosen to head a 12-member Rescue Committee comprising representatives of the various parties.

When the case closed, Eliezer immigrated to Palestine but continued to be attacked by right-wing and religious groups eager to discredit his father.

He was later a candidate for President in the 1952 presidential election alongside Yitzhak Ben-Zvi of Mapai, Peretz Bernstein of the General Zionists and Mordechai Nurock of Mizrachi.