Ethiopia's ambassador to the UK said the tabot - a tablet representing the Ark of the Covenant and the Ten Commandments - belonged in an Ethiopian Orthodox Church.
Hailemichael Aberra Afework told The Art Newspaper: "We are urging all those who hold items looted from Ethiopia to return them.
"This includes the tabot held at Westminster Abbey.
"We renew the call for restitution and urge the Abbey to return this sacred artefact, which holds so much significance in Ethiopia."
Made either of wood or stone, it is customary for any Ethiopian Orthodox Church to contain a tabot. They remain covered and can only be seen by priests.
The tabot at Westminster Abbey was offered a gift after it was taken by soldiers who fought against then-Abyssinia in the Battle of Magdala in 1868.
The then-head of the Ethiopian Orthodox Church, Abune Paulos met with the Abbey's receiver-general in 2007, when he called for the return of the tabot.
A spokesperson for Westminster Abbey told Premier: "The dean and chapter are very conscious of the sensitivity of the Ethiopian tabot, so steps were taken a number of years ago to ensure that the tabot, which is in a very sacred place, was properly covered and could not be seen by anyone."
They added that there are "no plans to change these arrangements".
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