Sudan's intelligence chief has ordered the release of all detainees held during the weeklong protests that rocked the North African country.

Tuesday's announcement came amid increasing international criticism of Khartoum's handling of the ongoing demonstrations.

"The chief of the National Intelligence and Security Service (NISS) issued an order to release all detainees held in recent incidents," the information ministry reported Sudan's intelligence and security chief Salah Gosh as saying.

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The protests, which began on December 19 after the government decided to triple the price of bread, have since turned into a nationwide movement calling for President Omar al-Bashir to step down.

Rights groups say NISS arrested more than 1,000 people, including protesters, opposition leaders, activists and journalists, as part of its clampdown.

Officials say 30 people have died in violence during the protests, but human rights groups have put the death toll at more than 40.

Protest anniversary

On Tuesday, hundreds of protesters turned up in and around the capital Khartoum, marching in memorial for those killed in past protests and reiterating their calls for al-Bashir's removal.

Al-Bashir, who took power in a 1989 coup, has said any change of leadership could only come through the ballot box. The 75-year-old leader is expected to run for another term in office next year.

The demonstration, called by unions and opposition activists fell on the anniversary of the 2005 killing of protesters in Port Sudan during an earlier period of popular upheaval.

In ensuing clashes with government forces, 21 demonstrators were killed, according to activists. Since then, every year on January 29, Beja tribesmen mark the deaths with a sit-in at Port Sudan.

"This sit-in is not just to mourn the 2005 deaths, but also to mourn the deaths of those who have died in the uprising since December," Beja activist Abdallah Mussa told AFP news agency from Port Sudan.

The opposition National Umma Party said in a statement that security forces surrounded its building in Omdurman and arrested several employees. It denounced the move but said it would not be dissuaded from "working to overthrow the regime and build a new Sudan".

'Credible and independent investigation'

Meanwhile, the United States has warned that Sudan's response to the protests might affect ties between the two countries.

Last week, the US expressed concern "about the increasing number of arrests and detentions" and urged Khartoum to free "all journalists, activists and peaceful protesters who have been arbitrarily detained".

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"We also call on the government to allow for a credible and independent investigation into the deaths and injuries to protesters," said State Department spokesman Robert Palladino.

The US has been slowly mending relations with Sudan after decades of tension, including over the presence of late al-Qaeda chief Osama bin Laden in the country in the 1990s and a military campaign in the western region of Darfur that Washington described as genocide.

Britain, Canada, Norway and the United Nations have also criticised the crackdown, along with human rights groups.

For years, anger has been mounting across Sudan over growing economic hardships and deteriorating living conditions.

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Al-Bashir has blamed the country's economic woes on Washington, which had imposed a trade embargo on Khartoum in 1997.

Washington lifted the embargo in October 2017, but that has failed to revive the country's economy hit by soaring inflation and an acute foreign currency shortage.