At least two of the pets were stabbed and three are understood to have died from their injuries.
The incidents were all reported within a short distance of Ditchling Rise in centralÂ Brighton.
A Sussex Police spokesman said: '˜Sussex Police have received further reports of injured or deceased cats following the suspected stabbing of a pet in Ditchling Rise,Â Brighton, on Monday (November 19).
'˜Two officers have now been allocated to investigate the reports and establish whether there may be links between those that have not been shown to be attacks by other animals or accidental injury.'
Pc Andy Chapman said: '˜We are taking these incidents very seriously and we have already spoken at the North Laine local action team meeting.
'˜In total, seven reports have been made since mid-September, of which two have been confirmed as highly likely to be stabbing injuries.
'˜We understand the impact and emotional distress caused to the owners of much-loved pets and we are determined to put an end to these attacks.
'˜However, we do need help from the public. I urge anyone with information or who believes that their pet has been the victim of a deliberate, malicious attack is asked to report online or call 101 quoting Operation Diverge.'
Tony Jenkins, of the animal charity Snarl (South Norwood Animal Rescue Liberty), which is investigating a series of cat deaths across the South East that it attributed to the '˜Croydon Cat Killer', said theÂ BrightonÂ attacks seemed unconnected.
He said: '˜We think it's a separate perpetrator because there are stab wounds and the injuries are different; there are not decapitations as seen in the other cases.
'˜Although it's horrible, it is not linked to the wider Croydon Cat Killer.'
In September, the Metropolitan Police discontinued their three-year investigation into 400 reports of cat deaths attributed to the Croydon Cat Killer and said the deaths were likely to have been caused by foxes and vehicle collisions.
Mr Jenkins said Snarl was continuing to investigate as there was '˜clear evidence'Â of human involvement.
He said: '˜Without a shadow of doubt, there is a pattern of behaviour around the killings.
'˜Police have resource issues with funding cuts and couldn't afford to investigate further and they took the easy route to blame foxes.
'˜There is clear evidence to suggest human interaction and we are continuing to investigate.'