Bashir made the comments in a speech broadcasted live on a national radio on Wednesday.
“They brought agents, thieves and hijackers, and they said Khartoum will be overthrown,” the president said.
However, he did not specify who those people were.
“But Khartoum could not be overthrown because it was guarded by God,” the president noted.
Bashir also said his government has plans to stabilize the economy and find solutions to outstanding problems.
Last month, the government cut gasoline subsidies, which led to an over 60-percent rise in fuel price. This brought thousands into the streets, with protests turning violent.
As the government tried to break up the rallies in the south of Khartoum, they spread to other parts of the country including Nyala, the capital of the restive state of South Darfur.
Activists say security forces have killed around 200 people. Sudanese authorities put the death toll at 70 and blame unknown gunmen for the killings.
The Sudanese government is trying to restore peace to the violence-hit regions.