Police have issued a warning after a suspicious man made several approaches to children in Dunedin over the last week. (File photo)

Dunedin residents are feeling on edge after a suspicious man reportedly approached four school children over the last week.

The latest incident happened about 8.30am on Tuesday near Warrender and George streets and was reported to police about 11am.

It followed another incident on Shetland St, in Wakari, on Monday, where a man told a child to come into his vehicle as he was looking for a lost puppy.

The child refused to get into the vehicle and the man then drove away.

READ MORE: Warning about suspicious man

A man also approached another child at the same time on September 4, on Three Mile Hill Rd in Halfway Bush.

A Dunedin mum told the Otago Daily Times her child was also approached on Monday afternoon, on Balmacewen Rd.

She said she had footage of the vehicle, described as a dark blue people mover, with silver-rimmed wheels, a dint on the boot, and tinted windows. She planned to give the footage to police on Tuesday afternoon.

Many schools in Dunedin have issued safety messages to students and parents.

Detective Sergeant Dylan Ross said it was not clear if the incidents were linked.

Each incident was being investigated individually and thoroughly, and police took the situation "very seriously".

"We understand that these types of approaches can cause a great deal of concern for parents, but our message to the community is to be alert, not alarmed."

Ross encouraged families to talk to their children about behaviours and actions that were inappropriate and made them feel uncomfortable, rather than concentrating on the types of people that could harm them.

"We want kids to be able to identify behaviours that make them feel uncomfortable, unsafe or scared and take action, remove themselves from the situation and tell someone."

Anyone who has an immediate concern for their safety should call 111 immediately.