Protesters demonstrating after Sudan's government scrapped fuel subsidies set fire to cars at a luxury hotel near Khartoum airport on Wednesday, after three people died in rioting.
The education ministry said schools in the capital would remain shut until September 30.
An AFP correspondent reported several users saying Internet access had been cut, but it was not immediately known if this was a fault or a deliberate move by the authorities.
The correspondent said the vehicles that were burned were in a car park just 500 metres (yards) from the international airport, and said police responded with tear gas.
A petrol station in the area was also set alight, the correspondent added, and some 20 protesters were arrested.
Two people have now been killed in the Khartoum area in riots sparked by the lifting of fuel subsidies, police and the family of one of the victims said Wednesday.
The deaths since Tuesday take to three the number of people who have died since demonstrations erupted in central Sudan on Monday before spreading to the capital.
On Monday, the government announced steep price rises for petroleum products after suspending subsidies in a bid to reform the economy.
On Tuesday, protesters ransacked and then torched offices of the ruling National Congress Party in Khartoum's twin city of Omdurman, witnesses told AFP.
"The people want the fall of the regime!" chanted hundreds of demonstrators, including students, echoing the Arab Spring mantra first heard in Tunisia in late 2010.
An AFP correspondent said around 1,000 demonstrators spilled into Omdurman's heavily populated Al-Thawra district and were confronted by anti-riot police.
The Omdurman protests lasted until around dawn on Wednesday.
One student was killed in the Omdurman, named to AFP by his family as Omar Mohammed Ahmed al-Khidr.
Police said that another man was killed in Khartoum, without naming him, and that other civilians and police were injured.
"Most areas in Khartoum (province) saw unrest and unauthorised gatherings aimed at damaging property and allowing looting, necessitating police intervention," a statement said.
It said one man was killed in the capital "while trying to steal the property of a citizen who fought back".
The protests first broke out in Wad Madani in Al-Jazeera state southeast of Khartoum on Monday, where one man died.
They later spread to the streets of Khartoum, Omdurman and Nyala, capital of South Darfur state.
A Nyala resident told AFP by phone that thousands of students filled the streets there and blocked a main road.
He estimated their numbers at 3,000 and said they were shouting "No to price hikes!" and calling for the ouster of the government.
Oil prices at the pump have shot up to 20.80 Sudanese pounds ($4.71) a gallon from 12.50 pounds ($2.83), while diesel has risen from 8.50 pounds a gallon to 13.90 pounds.
Inflation in Sudan is already running at 40 percent.
President Omar al-Bashir said on Sunday the subsidies had reached "a level that is dangerous for the economy".
Sudan lost billions of dollars in oil receipts when South Sudan gained independence two years ago, taking with it about 75 percent of the formerly united country's crude production.
Since then Sudan has been plagued by inflation, a weakened currency and a severe shortage of dollars to pay for imports.