President Mnangagwa, 81, is serving his second and last term after succeeding long time ruler Robert Mugabe following a military coup in 2017.
South Africa will hold the national and local government elections on May 29.
There has been uncertainty around Russia's allegiances in Sudan due to its ties with RSF Commander Mohamed Hamdan Daglo.
UN sanctions monitors have described as "credible" accusations that the United Arab Emirates had provided military support to the RSF.
For weeks, the RSF has been mobilising thousands of fighters on the outskirts of El Fasher in preparation for an attack.