Protesters, who are angry over rising food prices in the hemisphere's poorest country, have been demanding the resignation of Preval, who was elected in 2006.
The US also said it had suspended the operations of its embassy in Port-au-Prince, the Haitian capital, as violence continued.
A group of Haitian politicians has also called for Jacques-Edouard Alexis, Haiti's prime minister, to resign amid the growing unrest.
"We have written to Mr Alexis and we have advised him to resign in the next 48 hours," Andris Riche, a senior senator, said on Wednesday.
"It is not an ultimatum, it's advice," he said.
Hyppolite Melius, another senator who signed the letter, said Alexis could be forced out of office.
Police and UN peacekeepers patrolled in pickup trucks but were unable to control outbreaks of violence.
|Violence has gripped Haiti for days [EPA]|
Protesters continued to set tyres ablaze in Port-au-Prince, and gunfire was heard throughout the city's Petionville area, where many diplomats and foreigners live.
Several people were injured by bullets and rocks in the capital, including a Haitian police officer, Fred Blaise, a UN police spokesman said.
About 40 have been wounded since the unrest erupted on Thursday.
Radio stations also reported the looting of a government rice warehouse outside Port-au-Prince and the office of Petionville's mayor.
Protests were also reported on Wednesday in two northern towns, St Marc and Cap-Haitien.
"You haven't seen nothing yet," Jeanti Mathieu, a 22-year-old, said as he helped build a street barricade made of wrecked cars, concrete blocks and debris.
Ban Ki-moon, the UN secretary general, appealed for calm and said he "urges all demonstrators to refrain from any further acts of violence," his press office said in a statement.
He also condemned attacks against the 10,000-strong UN mission in Haiti (MINUSTAH) as well as against the Haitian government and private property.
The Haitian leader said his government could not afford to bow to demands that it lift all taxes on food imports.
Preval said money was too sorely needed for road building and other projects.
Food prices, which have risen 40 per cent on average globally since mid-2007, are causing unrest around the world.
They pose particular problems in Haiti, where most people live on less than $2 a day.
"I have five kids and I provide food if I can. Some days it's bread and sugar," said Paul Fleury, a 53-year-old who has been unemployed for a decade.