Sudanese security services have arrested more than 300 Sudanese and Chadians following the attack, the foreign ministry said.
An army spokesman said that as of Tuesday "there are no more JEM forces inside the capital, although there are some individuals hiding".
He said that the rebels had managed to infiltrate the area around the capital by wearing Sudanese army uniforms with civilian clothes underneath, arriving in small numbers and then regrouping.
In a telephone interview with Al Jazeera, Ibrahim said he was still in Omdurman and vowed to keep up the fight.
"It is true, we are still in the national capital. It is also true that we fought the Sudanese government there," he said.
As for why the group attacked Sudanese troops near the capital, he said it was "because the Sudanese government is not serious in exploring peaceful solutions to this cause".
Al Jazeera's Amr El Kahky, reporting from Khartoum, said a semblance of normality was returning to the capital.
People had begun to venture out and traffic was picking up, he said.
More than 220 people were killed in Saturday's raid and clashes outside the city over three previous days, as the rebel force headed from the remote west to Omdurman in at least 150 vehicles.
A military spokesman said 91 rebels, whom he referred to as "Chadian forces" following allegations of Ndjamena's involvement, were killed in Omdurman and "a lot more" in battles outside the city.
He said 34 civilians died in the fighting in Omdurman, including two Egyptians and two Senegalese, and that in total the army captured 68 rebel vehicles and destroyed 75.