The Israeli Government are to speed up the moving of the remaining 18,000 Ethiopian Jews to the Middle East.
However, the emigration of the Falasha Mura community would not start next week as had earlier been reported, says Israel’s foreign ministry.
Foreign Minister Silvan Shalom admitted at the end of a two-day Ethiopia visit, that the issue was a complex one.
The Falasha Mura are the last remaining Jewish community in Ethiopia and have long been persecuted for their beliefs.
The last mass emigration of Ethiopian Jews to Israel was in 1991.
There are around 80,000 Ethiopian Jews living in Israel, many of them airlifted there during times of crisis.
Ethiopian Foreign Minister Seyoum Mesfin, speaking alongside Mr Shalom, said a mass migration was not needed as Ethiopians were free to travel wherever they wished.
“The Ethiopian Government has no objection for the Ethiopian Jews to travel to Israel,” he said, but added that “in today’s Ethiopia, there is no need for an organised intervention as in the 1980s and 1990s”.
Mr Shalom visited the northern Gondar region on Wednesday to meet members of the Falasha Mura, many of whom were forced to convert to Christianity.
Israel organised the airlifting of 20,000 Ethiopian Jews to Israel in 1984 and another 15,000 members of the community in 1991.
Many were resettled on the volatile West Bank and have suffered from discrimination and high unemployment.
Some Falasha Mura say the Israeli Government has prevented their relatives from joining them.
The authenticity of their Jewishness has also been challenged by religious figures.
The Israeli Government announced last year that 20,000 more Ethiopian Jews could come to Israel under the country’s law of return which says that Jews anywhere in the world have the right to Israeli citizenship.
But Ethiopia blocked the move, arguing that a migration en masse was unnecessary when Ethiopians were free to leave the country.