A man in his twenties was arrested by Greater Manchester Police after allegedly attacking two women in separate parks in Rochdale.
The incidents are said to have occurred several hours apart, with each woman alone in the park at the time.
The suspect remains in police custody and is being investigated on suspicion of attempted rape in two counts.
Investigations are ongoing and, in line with the presumption of innocence, the man is considered innocent until proven guilty by a court.
Greater Manchester Police said they have increased patrols in the affected parks to reassure the public.
A spokesperson for the Crown Prosecution Service stated that a decision on any charges will be made only after the investigation concludes.
Victims of sexual violence are being offered support from local counselling services providing confidential help and advice.