A young girl was indecently assaulted in a “horrendous” attack in Flinders Street in the Melbourne CBD soon after the New Year’s Eve midnight fireworks, Victoria police have said.

The girl, who deputy commissioner Shane Patton said was “just less than a teen”, was assaulted in public by a stranger who is yet to be identified by police.

She was in the city to celebrate New Year’s Eve and was “with adults at the time”, Patton said.

Patton said it was a “horrendous crime”.

“She was indecently assaulted, sexually assaulted, by an unknown offender and our sex crimes unit is actively investigating that matter,” he said. “We will continue to pursue and see whether we can apprehend that offender.”

It was the most serious crime in what police said was an otherwise quiet New Year’s Eve.

Only 59 people were arrested throughout Victoria, down from 288 on New Year’s Eve last year, although Patton told reporters on Tuesday the reduction could be partly due to better data gathering, separating offences specifically related to New Year’s Eve from crimes that just happened to occur on the night.

The number of people arrested for being drunk in a public place reduced by almost two-thirds – 37 compared with 99 in 2017.

Patton said preliminary results showed there were fewer than 10 assaults.

Police in Victoria also issued 57 infringement notices for behavioural offences and 43 for traffic offences directly connected to New Year’s Eve celebrations.

Ambulance Victoria received 1,089 emergency callouts from 6pm to 3am, including a man who was critically injured after falling and hitting his head at Falls Festival in Lorne about 10pm, and a man in his 60s who was taken to hospital with injuries to his face caused by a firework in Altona Meadows.

A seven-year-old boy was also hit in the face by debris from fireworks at Loch Sport on the Gippsland Lakes and received minor injuries.

Police in Sydney arrested 35 people who were in the city or on the foreshore during the firework displays, mainly for drug offences.

New South Wales police said they also charged six people with affray, a further six with offensive behaviour, four with resisting arrest and assaulting a police officer, and two with common assault.

NSW police acting deputy commissioner Mark Walton said the crowds in Sydney were also generally well behaved.