It comes as detectives released CCTV images of two men they want to speak to in connection with a sex attack in the city's Govanhill area.
Detectives are hunting for two men after a 24-year-old woman was raped in Dixon Road, between 1am and 2am on Monday.
The men pictured were seen in the company of the victim on Allison Street near to Cathcart Road and in Cathcart Road near to the Spar Shop.
The attack came a week after three men dragged a 33-year-old woman off the street and sexually assaulted her in nearby Toryglen.
The victim was raped in Edinbeg Avenue between midnight and 3am on Saturday May 10.
Police do not believe the attacks are linked.
More than 1000 people have signed up to a mass march in response to the attacks.
Superintendent Brian McInulty said several lines of inquiry were being followed.
He said: "I understand that members of both communities may be worried following these assaults, however, I would like to take this opportunity to reassure the public that we have two teams of officers from the Rape Investigation Unit dedicated to these enquiries.
"Enquiries are continuing and several lines being investigated.
"There is nothing to suggest that these incidents are linked."
Extra police will be patrolling the streets in both areas to help ease concerns.
Meanwhile, anti- violence campaigners are preparing for a midnight march on Monday June 9 at Queen's Park.