He has blamed external factors for the collapse, but protesters say it stems from decades of kleptocratic, incompetent rule. Their frequent chant during marches — before riot police arrive with tear gas and sometimes bullets — is, “Just fall, that is all!”

Protest leaders say that more than 1,000 people have been arrested in a crackdown led by the feared National Intelligence and Security Service. Internet access has been restricted in an effort to block social media posts used by the mostly young protesters to organize demonstrations.

The government has said that 31 people have died in protest-related violence. Human Rights Watch has put the toll at 51 people killed since mid-December.

On Friday, Mr. al-Bashir stumbled several times as he read his speech. In an attempt to mollify the protesters, he offered prayers for those killed and announced plans for economic reform under the new government, which has yet to be fully formed. He invited the opposition “to move forward and engage in dialogue regarding the current issues of our country.”

In recent years, Mr. al-Bashir has fired or marginalized potential rivals for power, and little in his long rule suggests a new willingness for rapprochement.

Mr. al-Bashir came to power in a military coup in 1989, and since then Sudan has endured famines, American missile strikes, isolation and a civil war that led to the independence of South Sudan in 2011. Two years before that, the International Criminal Court ordered Mr. al-Bashir arrested on charges he played an “essential role” in atrocities, including murder, rape, torture and displacement of civilians during the conflict in the Darfur region of Sudan.

In 2017, the United States lifted sanctions on Sudan, but the relief failed to stem a steep economic decline. Mr. al-Bashir has lobbied the State Department to remove Sudan from a list of state sponsors of terrorism, a factor in the country’s economic woes.