Two arrests have been made over the Bonfire Night disorder in the Niddrie area of Edinburgh.
A group of 50 youths threw fireworks and petrol bombs at riot police.
Community Safety Minister Siobhan Brown told MSPs there had been two arrests and more were expected in the coming days. Police inquiries are continuing into the incident.
Justice Secretary Angela Constance has said she is "open to discussion" about a ban on fireworks.
She said ministers lacked the powers for a ban but that she was "open-minded" about the idea.
Eight police officers suffered minor injuries in incidents in Edinburgh and Glasgow.
Ms Constance was speaking after City of Edinburgh Council leader Cammy Day said he would look at bringing in powers designed to create firework control zones.
He also said he supported a ban on the sale of fireworks to the general public.
Speaking on the BBC's Good Morning Scotland programme, the justice secretary praised Police Scotland and the Scottish Fire and Rescue Service for their efforts and addressed calls for an outright ban on the sale of fireworks to individuals.
"I'm open minded about it. Open to discussion. It's not within our powers for an outright ban but open to discussion," Ms Constance said.
The Scottish government brought in a new law last year which heavily restricts the sale of fireworks and made it an offence to buy them for young people.
But Ms Constance disputed claims by both the Fire Brigades Union (FBU) and the former children's commissioner for Scotland that cuts in education, outreach and preventative services contributed to violence against the emergency services.
She told the programme: "This government continues to invest in preventative services, whether that's through the cash back programme that supports over 33,000 young people, whether it's the violence reduction framework, where there's investment of £2m.
"There is that emergency response to incidents of serious disorder and it's important that the law is enforced."
Speaking on Monday, Mr Day called for action to prevent a repeat of the violence.
He said: "The public sale of fireworks needs to be reconsidered. Because if we don't do something that's quite drastic I would hate to think what happens the next time.
The council leader has asked for a briefing on Sunday's events, which saw 50 youths threw fireworks and petrol bombs at riot police in the Hay Avenue area of Niddrie.
Elsewhere, two police vehicles were damaged after being struck with bricks in the Beauly Square area of Dundee and a street fight involving about 20 youths took place in Glasgow's Barmulloch.
Four people, including a police officer, were taken to Glasgow Royal Infirmary for treatment.
Police Scotland said officers faced "unprecedented levels of violence".
Assistant Chief Constable Tim Mairs said the actions of adults caught on camera directing children to commit crimes was tantamount to "child abuse".
And First Minister Humza Yousaf condemned the "thuggish and reckless behaviour" in parts of Scotland, particularly in Niddrie.
He said those involved in the disturbances should "feel the full force of the law".
Police Scotland has appealed for anyone with information on Sunday's events to contact them.