Police have now released a picture of the man they want to find following the incident at approximately 12.30pm on Wednesday 18 October.
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It happened when two 16-year-old girls and two 17-year-old girls were approached by a man unknown to them in Cosham High Street who followed them to a bus stop making abusive comments.
When they got off the bus outside Queen Alexandra Hospital they saw the man again and he made more abusive comments towards them. None of the girls were hurt, police said.
A police statement said: “Officers investigating a public order incident in Portsmouth would like to speak to him in connection with their enquiries. We have been carrying out enquiries and now have this image of a man, seen in the area at the time, who we would like to speak to in connection with this incident.
“Is this you? Do you recognise him or do you have any information which may assist our investigation?
“If so, please call 101 quoting reference 44230426997. Alternatively, go online and submit information via https://www.hampshire.police.uk/tua/tell-us-about/cor/tell-us-about-existing-case-report/”