Members of the National Intelligence and Security Service (NISS) and police raided the flat in the south Khartoum residential district of Arkawiet after local police reported a blast in the building at around 2:00 am (23:00 GMT Saturday).
"During the raid, materials used to detonate high intensity blasts were found, along with some foreign passports," a police statement said.
Further investigation revealed that a man had been wounded by the blast, which happened while he was allegedly assembling the explosives.
Police were hunting for him and for others, it said, without elaborating either on the fugitive or on the passports that were found.
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Earlier today, dozens of policemen and security agents cordoned off the area, and an AFP correspondent reported that security agents emerged from the building with plastic bags containing materials found in the apartment.
Residents said that apart from Sudanese families, many Egyptians and Syrians also lived in the area.
Officials have regularly claimed to be stepping up efforts to fight extremism in the region, although Washington continues to list Sudan as an alleged state sponsor of terrorism since 1993, a charge Khartoum steadfastly denies.
Sudan is one of seven mainly Muslim countries on the January 27 travel ban that US President Donald Trump imposed. The ban is currently suspended as the issue is played out in the courts.