His departure has been confirmed by the Libyan Football Federation and on Wednesday by Belgian Amrouche, who told Reuters he was frustrated by working conditions with the team.
The 50-year-old, who was born in Algeria, was only appointed in May and his first match in charge last month saw Libya force a 0-0 draw in South Africa.
Forced to play all their home qualifiers at a neutral venue because of the tenuous security situation in the North African country, Libya travel to face Nigeria on Friday and then play them again in the return in Sfax, Tunisia on Monday.
Libya have four points from their first two games in their bid to qualify for the 2019 finals in Cameroon, ahead of South Africa on goal difference with Nigeria one point behind.
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The Seychelles are last in the group without any points.
The top two teams qualify for the finals next June.
(Reporting by Mark Gleeson in Cape Town; Editing by Peter Rutherford)
