Moroz ran as a presidential candidate as a nominee of the Socialist Party of Ukraine in the 1994 and 1999 elections, he came third both times, with 13.04% of the vote in 1994 and 11.29% in 1999.
Как в первом, так и во втором случае он занял третье место, получив соответственно 13,04 % голосов избирателей в 1994 и 11,29 % в 1999.