* Police fire on students, public at university and in capital
* PM O'Neill says won't stand down over corruption allegations
* Dozens wounded, as many as four reported dead
* Rioting, violence spreads beyond capital, businesses close (Adds U.N. secretary-general comment in paragraphs 9-10)
By Colin Packham and Matt Siegel
SYDNEY, June 8 (Reuters) - Dozens of people were wounded in Papua New Guinea on Wednesday after police opened fire on a student demonstration in the capital and riots erupted across the country, but officials said earlier reports of up to four dead were incorrect.
A groundswell of political unrest in recent weeks has surged in the country, just to Australia's north, amid calls for Prime Minister Peter O'Neill to resign over corruption allegations.
Students and officials said police fired on the public and used tear gas to disperse crowds during a protest at the University of PNG's Waigani campus in Port Moresby. Protests were later reported in the PNG highland cities of Goroka and Mt. Hagen, and in Lae on the north coast.
"Now there is a very big clash with the public and with the police just outside the Port Moresby General Hospital," a hospital official told Reuters by telephone soon after a group of wounded students were taken there for treatment.
"There is also shooting going on, open gunfire."
The government said initial reports that up to four people had been killed were incorrect. An official at the Port Moresby General Hospital said 38 casualties had been treated there, including four with bullet wounds, but no deaths.
O'Neill later issued a statement in which he refused to stand down.
"The facts relayed to me are that a small group of students were violent, threw rocks at police and provoked a response that came in the form of tear gas and warning shots," he said.
United Nations Secretary-General Ban Ki-moon on Wednesday expressed concern about the clashes.
"He calls for calm and stresses the importance of respect for peaceful protest and freedom of assembly, and a commitment to rule of law, dialogue and non-violence," Ban's spokesman Stephan Dujarric said in a statement.
Papua New Guinea, formerly administered by Australia, struggles with endemic violence and poverty despite a wealth of mineral resources. It is ranked 139 out of 168 in Transparency International's corruption index.
Wednesday's events echoed a similar confrontation in 2001 when police opened fire on anti-government student protesters. A full account of that incident has never been given.
The PNG Police Ministry did not directly address the shooting, but said in a statement that students or others who had engaged in subsequent vandalism or assaults would face the "full force of the law."
"Police are now investigating the string of offenses that have been committed and arrests will be made," it said.
The Australian government said there had been an "unconfirmed number of deaths and serious injuries," while the United States and Britain told its citizens to avoid areas hit by violence. "The situation is still volatile and could escalate at any time," the U.S. Embassy said in a statement.
Qantas Airways QAN.AX and Virgin Australia VAH.AX said they had canceled one flight each from Australia to Port Moresby and were assessing whether to fly on Thursday.
PEOPLE FLEEING
Hubert Namani, a lawyer and business leader, said public transport had been halted in Port Moresby and businesses shut.
"People are looting and rioting and sort of revolting, so the police are now caught trying to manage all of that," Namani told Reuters by phone from the capital.
Student protest leader Noel Anjo said the violence began when students started a march from the campus toward the parliament building in Port Moresby, where police had set up a roadblock.
"Police did not like that idea and started assaulting the students, punching them, hitting them with the gun butts, before firing shots at them," Anjo said. "The students were running for cover in all directions, but I saw some people badly wounded."
TEAR GAS, GUNFIRE
Video showed students fleeing amid clouds of tear gas and the sound of gunfire. Pictures showed several men with what appeared to be serious stomach, chest and leg wounds.
Thousands of students across PNG have been protesting and boycotting classes for weeks amid growing political unrest.
O'Neill, who came to power in 2011 promising to reign in corruption, has faced allegations he authorized millions of dollars in fraudulent payments to a leading law firm.
In 2014, an anti-corruption watchdog issued an order for his arrest over the incident, which O'Neill denies. He refused to submit to the warrant and ordered the watchdog stripped of its funding.
Most of Papua New Guinea's seven million people live subsistence existences in isolated mountain villages and scattered tropical islands.
Despite that, an energy production boom, which includes Exxon (NYSE:XOM) Mobil's XOM.N $20 billion LNG plant, has fueled annual economic growth of almost 10 percent a year for the past three years.
Exxon and partner Oil Search OSH.AX said there had been no damage or impact to their operations, as did Newcrest Mining NCM.AX , which operates two remote gold mines in PNG.
"This is going to get worse before it gets better," said Greg Anderson, executive director of the Papua New Guinea Chamber of Mines and Petroleum in Port Moresby.
"Incidents like this trigger paybacks, which could easily spiral out of control," he said.
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