Sudan's President Omar al-Bashir has ordered an investigation into "recent events" after two weeks of violent protests against his 29-year autocratic rule, as he seeks to placate popular anger over worsening economic conditions.

The state news agency reported late Monday that al-Bashir has tasked Justice Minister Mohammed Ahmed Salem with leading the investigation, without providing further details on the subject of the probe.

Twenty-two political parties and groups meanwhile said they will call on Bashir to step down and transfer power to a "sovereign council" and a transitional government that would set a "suitable" date for democratic elections.

The parties include some Islamist factions that were once allied with al-Bashir, who seized power in a 1989 military coup, as well as breakaway groups from large traditional parties, like the Democratic Unionist and Umma parties, which did not join in the call.

"It is well known that the (current) regime does not have the common economic tools to halt the deterioration," they said in a memorandum they plan to present to al-Bashir on Wednesday. "The regime, in its present composition and given its political, economic, regional and international isolation, cannot pull through this crisis," it said.

It warned that failure to transition to a new political system would have "dire consequences" for Sudan.

The parties said the proposed administration would introduce freedoms, democracy and halt the ongoing strife in the western regions of Kordofan and Darfur, and the Blue Nile region south of the capital, Khartoum.

There was no immediate reaction from the government to the memorandum, which was read to reporters in a Tuesday news conference in the Sudanese capital.

Western nations, including the United States and Britain, and rights groups have called on authorities in Sudan to investigate the use of lethal force by security forces against demonstrators. Some activists have speculated that al-Bashir's political rivals may have engineered an acute shortage of fuel and other basic commodities to whip up anger against the government.

Authorities have said that 19 people died in the protests, while Amnesty International said it has "credible reports" that 37 died in the first five days of protests. Human Rights Watch said Monday that independent groups have put the death toll at 40 since the protests erupted on Dec. 19.

Al-Bashir on Monday sought to defuse the anger sweeping the country, promising better days ahead and pledging more "transparency, effectiveness and justice in all our national institutions" in an address to the nation marking the anniversary of Sudan's independence 63 years ago.

"Our country is going through pressing economic conditions that have hurt a large segment of society," he said. "We appreciate this suffering, feel its impact and we thank our people for their beautiful patience."

Al-Bashir said the 2019 budget would maintain state subsidies on many commodities, raise wages, refrain from introducing new taxes and do more for the poorest. He did not elaborate.

Sudan's economy has stagnated for most of al-Bashir's rule. He has also failed to unite or keep the peace in the religiously and ethnically diverse nation, losing three quarters of Sudan's oil wealth when the mainly animist and Christian south seceded in 2011 following a referendum.

Critics say rampant corruption is eating up a significant part of government funds and engineering shortages of basic items to manipulate prices. The protesters have been chanting against the "government of thieves."