Ukraine refuse to accept Markevich resignation
The FA said on its official website the organisation would not accept his decision to stand down.
On Tuesday, the FA ruled a 2008 match between Metalist and Karpaty Lviv had been fixed and punished a number of officials and players. Markevich, however, was not implicated.
"Ukraine's Football Federation (FA) has completely discredited itself with the recent ruling and I have no moral right to work for an organisation that is purposefully destroying Kharkiv football," said Markevich earlier on Saturday.
The 59-year-old, who has led the national team since February, said he would stay on as Metalist coach.
Ukraine are co-hosting Euro 2012 with Poland.