Police are now going through CCTV footage from the nearby Canterbury Museum, and trying to get footage from other city cameras to get a look at the suspect.
Detective Sergeant William McIvor says the police intel section is also looking at any other previous events which may be related to "see if we can come up with some suspects that way".
But police say the small children are the key to the inquiry.
"We're really reliant on the interviews with the two children. Hopefully that will bring some more clarity," Mr McIvor said.
He was "pretty comfortable" the man was not known to the children.
Police spoke to the children's mother yesterday, Mr McIvor said.
"They appeared to be ok," he said.
"We'll get a better indication of that when they're interviewed.
"Sometimes these things don't come to the forefront until a couple of days later, so we'll see how they're doing then."
Mr McIvor appealed for the public to come forward who were in the park around 2pm when the incident occurred.
The offender would have stuck out, he said, given that it was a hot day and he was wearing such thick clothing.
He urged witnesses to come forward and contact police on (03) 363 7949 or anonymously on Crimestoppers on 0800 555 111.
"We'll be continuing with zest on this," Mr McIvor said.