The call, made by DUP MLA William Hay, comes amid concerns arising from an increase in incidents of anti-social behaviour.
Speaking to the Sentinel , Mr Hay said a family living in the Bonds Hill/Clooney Terrace area of the Waterside were now selling their home of thirty years because of ongoing anti-social problems.
"The situation arising from the Clooney Terrace area is a very sad one. This has always been a close knit, family friendly community and it is tragic to learn a family have been forced into selling their home while the perpetrators are seemingly allowed to continue their antisocial behaviour.
"There is a very real sense of frustration in the area, and across Londonderry."
The Speaker of the Stormont Assembly said there was now an onus on landlords to help safeguard local communities.
"It is up to landlords to know who they are renting homes to. There is a huge responsibility on them to do a background check on tenants. Some kind of mechanism aimed at protecting communities needs to be put in place.
"Some landlords need to become more socially responsible."
Mr Hay also said he was meeting with the PSNI later this week to address concerns about anti social behaviour.
He said said people felt let down by the police response to problems in the area.
But a PSNI spokesman said police were committed to working in partnership with the local community and all interested parties to try and address this issue.
"Dedicated Neighbourhood Policing Teams work with local communities, councillors and representatives to address all issues of concern.
"While efforts are made to respond to every call as quickly as possible the PSNI is an emergency service and calls must be prioritised as and when they come in."
He said officers were aware of the impact of antisocial behaviour on communities and called on everyone to accept a responsibility in tackling the issue.
"We would appeal to all local residents to work with us, and to provide us with information which will help us bring those responsible for anti-social behaviour and criminal activity before the Courts."
Anyone who has any information regarding anti-social behaviour is asked to contact the police on 0845 600 8000, or the 'Crimestoppers' charity on freephone 0800 555111