Kale Kaihura, the police inspector-general, condemned the shootings and said officials would investigate the incident.
"I have instructed the criminal investigation department director to investigate all those who shot at people," he said.
"All those involved will be arrested and punished."
Security forces had earlier used tear gas to disperse members of the Baganda ethnic group angry at the destruction of the tombs of the country's largest historic kingdom.
Malcolm Webb, a Kampala-based journalist, told Al Jazeera that the burial site of the traditional kings represented 200 years of the group's cultural heritage.
He said members of the group suspect the fire was caused by arsonists.
Buganda is one of Uganda's four historic kingdoms and the Baganda are the biggest ethnic group in the country.
The burial site of Kasubi, designated as a world heritage site by Unesco, the UN cultural agency, is an important tourist site housing the burial grounds of four former kings of Buganda. The last king was buried there in 1971.
Baganda have previously complained that the government has tried to expropriate the kingdom's land and have been involved in disputes over the influence of Buganda's traditional leaders.
A spokesman for the Buganda kingdom on Wednesday described the fire as "an attack on Buganda", whose people are concentrated in the south of Uganda and Kampala.
"This fire is very strange given what we [the Baganda] have been going through," Peter Mayiga said without giving further details.
Kale Kaihura, the chief of the Uganda police, refused to confirm reports that the blaze was started deliberately and said his officers were still investigating the cause of the fire.
|Uganda's police chief has said officials are still investigating the cause of the blaze [AFP]
He said however that firefighters had been prevented from reaching the site in time to put out the blaze before it gutted the burial site late on Tuesday.
"When the fire broke out, police were called in and got there in time but the fire brigade was obstructed by a hostile crowd, three trucks were damaged and a fireman injured," Kaihura told the AFP news agency.
Wednesday's violence triggered fears of renewed tension between the government and ethnic Baganda, who accuse the government of undermining their kingdom.
Last September, riots in Kampala left at least 17 people dead after the government prevented Ronald Muwenda Mutebi, the current Buganda king, from visiting a district near the capital.
The government said the district had its own traditional ruler and it did not owe allegiance to the king.
The king holds a largely ceremonial position in Uganda, but wields considerable influence among his people.
Monarchies were restored in Uganda in 1993 after they were banned in the 1960s, but they are not allowed to participate in elective politics by campaigning or fielding candidates.