Suleiman, in a statement Wednesday, said he didn't feel the time was right to launch a bid for presidency. His supporters, however, said they would continue to rally for his candidacy.
"He is a fighter, a military commander who should not leave his soldiers in the battle like that," Samel el-Ashy, director of the Revolutionary Front to Support Omar Suleiman's Presidency, told Egyptian news service al-Ahram.
"I cannot refuse people's will Suleiman was quoted by the Egyptian news service as saying, "Even though I said in my previous statement that I will face a lot of troubles and difficulties."
Suleiman, during last year's trial of former regime officials, suggested former Interior Minister Habib el-Adly was tied to police assaults on demonstrators during last year's revolution.
Former Arab League Secretary-General Amr Moussa, former Foreign Minister Ahmed Shafiq and former Muslim Brotherhood financier Khairat al-Shater are among those who've announced candidacies for president.
Suleiman said he'd back out if he didn't collect the prerequisite 30,000 signatures backing his candidacy by the weekend, however.
Presidential elections in Egypt are scheduled for May.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Biologists detail four new deep-sea 'killer sponges'