"We want to see the benefit of our oil wealth distributed evenly," one protester yelled over a loudhailer near the port. "We want to see a scale-down of expatriates in Oman so more jobs can be created for Omanis."
Peaceful protests spread to other cities, with hundreds gathering outside a state complex in the capital Muscat and elsewhere.
The unrest in Sohar, Oman's main industrial centre, was a rare outbreak of discontent in the normally sleepy sultanate ruled by Sultan Qaboos bin Said for four decades, and follows a wave of pro-democracy protests across the Arab world.
The sultan, trying to calm tensions, on Sunday promised 50,000 jobs, unemployment benefits of $390 a month and to study widening the power of a quasi-parliamentary advisory council.
While hundreds of demonstrators blocked roads near the port, hundreds more were at the main Globe Roundabout, angry after police opened fire on Sunday at protesters.
Police fired tear gas as around 200 protesters near a police building, which demonstrators had set fire to a day earlier.
Graffiti scrawled on a statue said: "The people are hungry." Another message read: "No to oppression of the people."
"There are no jobs, there's no freedom of opinion. The people are tired and people want money. People want to end corruption," said Ali al-Mazroui, 30, who is unemployed.
"We want a change of constitution, an elected government, and ministers standing in the way of development to go," said Zakaria Mharmi, a doctor at Sultan Qaboos Hospital.
"We are also calling for the police not to repeat the violence they demonstrated on Sunday," said Mharmi, who was among around 250 protesters outside the Shura Council building. "Protesters must be peaceful. They are not serving our cause if they are violent."
LOOTING IN SOHAR
In Sohar, looters earlier rushed in to scavenge a smouldering supermarket set alight by protesters. Two government buildings were also set ablaze on Sunday.
One woman stacked up singed cartons of eggs, powdered milk, orange juice and cream cheese in the store, while others walked over shattered glass pushing trolleys loaded with food out of the door. The security forces were absent.
"There is no security. I want to live. It's normal," said 28-year-old Youssef, who is unemployed, as he left the market carrying 10 bottles of juice.
The unrest pushed Oman's main stock index 4.9 percent to a seven-month low, its biggest drop in over two years.
Sultan Qaboos, who exercises absolute power in a country where political parties are banned, shuffled his cabinet on Saturday, a week after a small protest in the capital Muscat gave the first hint that Arab discontent could reach Oman.
Mostly wealthy Gulf Arab countries have stepped up reforms to appease their populations following popular unrest that toppled the leaders of Tunisia and Egypt and is threatening Libyan leader Muammar Gaddafi's grip on power.
Oman is a non-OPEC oil exporter which pumps around 850,000 bpd, and has strong military and political ties to Washington.
Sultan Qaboos appoints the cabinet and in 1992 introduced an elected advisory Shura Council. Protesters have demanded the council be given legislative powers and on Sunday Qaboos ordered a committee to study increasing its authority.