"I announce imposing a state of emergency across the country for one year", Bashir said in a televised address to the nation from the presidential palace in Khartoum.
Bashir who seized power in a 1989 coup said on Friday that he would postpone pushing for constitutional amendments that would allow him to seek a third term in office.
Sudan's President Omar al-Bashir in October 2018 lifted a 17-month long ban on agricultural imports from Egypt, during an official visit by Egyptian President Abdel Fattah al-Sisi to Khartoum.
While "some have exploited the protests to cause hate and violence", al-Bashir said, "we understand the demands of the youths".
The state of emergency will give the security forces a free hand in cracking down on protesters and carrying out detentions and it places heavier restrictions on the press and opposition parties. Amnesty International, which accused Sudanese security forces of a "deadly onslaught", said more than 40 people have been killed in the protests since mid-December. Protests have been ongoing since mid-December.
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The Sudanese Professionals Association (SPA), the main protest organizer, issued a call for additional demonstrations. Without amending the constitution, he can't run for a third term.
Activists say almost 60 people have been killed since the protests began, while authorities put the death toll at 31.
"The demands of this revolution are clear. foremost that this regime and its head step aside, including its repressive institutions", the SPA said in a statement, according to a Reuters report on Friday. On Friday, he once again warned of chaos similar to the Arab Spring uprisings that led to civil wars in countries like Libya, Syria and Yemen.
As he was speaking in the presidential palace in Khartoum and in other districts, dozens of protesters were already taking to the streets chanting, "just fall".
"What al-Bashir presented are tactics to keep his regime alive", said the leader of Umma Party, Mubarak al-Mahdi.
Al Jazeera's Hiba Morgan, reporting from Khartoum, said it would likely become increasingly hard for protesters to continue their demonstrations as the state of emergency kicks in. He has remained resistant to stepping down, saying that change can only come through elections.