Shalom toured the home region of Ethiopia's Jewish community in Gondar on Wednesday on what is the first visit by an Israeli foreign minister to sub-Saharan Africa in 13 years.
Shalom, who arrived in Addis Ababa on Tuesday evening on a three-day trip, will hold discussions with Ethiopian Prime Minister Meles Zenawi and Foreign Minister Seyoum Mesfin.
A foreign ministry official in Jerusalem said a large part of the trip would involve discussions over the possible immigration to Israel of members of the Falasha Mura.
"It is an important element in strengthening relations with Africa in general and Ethiopia in particular," the official said.
About 80,000 Ethiopian Jews currently live in Israel, many of them taken there in massive airlifts during times of crisis in Ethiopia over the past 20 years.
The last mass migration of Ethiopian Jews was in 1991, when Israel organised an airlift of 15,000 people who had fled fighting at the end of Ethiopia's civil war.
Israel's law of return says that Jews anywhere in the world have the right to make the aliyah (ascent) to Israel and claim citizenship.
Many Israeli politicians are deeply concerned about Jews' lower population growth compared to Palestinians and fear losing the country's Jewish majority.
Several members of the Falasha Mura were forced to convert to Christianity in the 19th century, but now wish to assert their Jewishness and emigrate to Israel.
PM Ariel Sharon is determined to
maintain a Jewish majority in Israel
Most of the Falasha Mura who were unable to prove their Jewish roots have not been allowed to emigrate to Israel, even though many have family ties to the Ethiopian Jews who had left in earlier emigrations.
The essentially rural Falasha Mura community has had to bridge a wide cultural gap and has faced a difficult integration into Israeli society, where the Ethiopians suffer from discrimination and high unemployment.
In February 2003, Ethiopia blocked an Israeli plan to move about 20,000 Falasha Mura to Israel, arguing a mass migration was unnecessary when people were free to leave Ethiopia in the normal way.