"I announce imposing a state of emergency across the country for one year," Mr Bashir said in a televised address to the nation on Friday.
He also asked parliament to postpone constitutional amendments that would allow him to run for another term.
Mr Bashir has been the focus of anti-government protests in recent weeks.
He said the demonstrations were an attempt to destabilise the country and earlier insisted that there could only be a change of government if it was determined through the ballot box.
The demonstrations started over cuts to bread and fuel subsidies in December but later morphed into anger at Mr Bashir's 30-year rule.
More than 1,000 people are reported to have been detained since the protests began. Rights groups say more than 40 people have been killed in clashes with security forces.
Earlier on Friday, the head of Sudan's National Security and Intelligence Services (NISS) said that Mr Bashir would be stepping down, according to reports.
Protest organisers have vowed to continue demonstrating until Mr Bashir steps down, AFP news agency reported.
Mr Bashir, 75, had initially struck a defiant tone after winning elections several times since coming to power in a coup in 1989.
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