The officers had been sentenced this month to up to five years in prison by a military tribunal, the Sudan Tribune reported Thursday.
Al-Bashir ordered them released immediately. He also changed their expulsion from the army to a discharge, which would allow them to return to military service.
The deputy chairman of the Islamist Sa'ihoon organization, Mohamed Daffa-allah, welcomed al-Bashir's move and called on the president to begin comprehensive political, economic and social reforms. He also said al-Bashir should end the civil war and involve all political groups in the drafting of a new constitution.
Seven officers of the National Intelligence and Security Service, including the agency's former director, and six civilians remain jailed for their involvement in the November coup plot.
A member of a team mediating between the government and the Sa'ihoon group said in a statement they were working to gain their release.