Detective Senior Sergeant Mark Worner said a man confronted a woman at her car in the Jellie Park Recreation and Sports Centre carpark on Ilam Rd about 5.30am.
The man is then said to have fled on a bicycle through Jellie Park on to Greers Rd.
At about 5.50am, a man tried to abduct a second woman, who was jogging, at the entrance to Ray Blank Park on Maidstone Rd, according to police.
The woman fought off the man and a member of the public driving past stopped to help her, Worner said.
The man got back on his bicycle and rode off down Maidstone Rd towards Avonhead.
A member of the public followed him in their car and saw him ride into a cul-de-sac nearby, police said.
Police are yet to speak to this witness and encourage them to phone Canterbury Police on 03 363 7400 immediately.
Worner said he would like to thank the person who stopped to help the second victim and asked that anyone who saw either event to call the Christchurch Police on 03 363 7400.
"We ask these people to contact us right away, their assistance this morning has been invaluable," he said.
"It's important to remember that people should be alert, not alarmed following these incidents."
