The 70-year-old Uruguayan apologised for the poor results and announced his intention to quit after the 2-1 defeat in their Group F qualifier last month.
Markarian took over in February from Claudio Ranieri, who was appointed at Leicester City earlier this month, but failed to lift Greece from the bottom of the group, securing only a 0-0 draw in Hungary before the 2-1 defeat in the Faroes.
Ranieri was suspended in November after the tiny island nation beat the Greeks 1-0 in Athens last November.
Romania lead the group with 14 points from six matches, one ahead of Northern Ireland, while Greece are last with only two points.
Greece face Finland at home on September 4 before visiting group leaders Romania three days later.