"The council have gone as far as they can (to meet residents' concerns) within the law and we understand that."
Residents of the estate had taken to the streets for the last seven nights, calling for alleged sex offenders to be removed from the area, but stopped after meeting the local council.
The protests were sparked by the News of the World's publication of names and locations of 200 convicted sex offenders.
The question of public access to details of sex offenders is to be discussed at a conference of the National Association of Ex-Offenders on Friday.
The mother of murdered schoolgirl Sarah Payne appealed for an end to violent anti-paedophile demonstrations.
"Stop the violence. We won't change the law if this goes on," Sara Payne said.
"Write to Tony Blair, write to Jack Straw. We're not going away, we will be here until the law changes.
"Don't riot - you are giving people a reason to be against you."
Protests halted
Although incidents relating to the newspaper campaign have occurred across the UK, attention has focused on the protests in Portsmouth.
Local resident and protest spokesman Barry Pettinger said after the council meeting that he hoped it was the end of the protests.
He said, "All our group's protests will stop for the immediate future.
"The council have gone as far as they can (to meet residents' concerns) within the law and we understand that."
A list of 11 names of suspected paedophiles, drawn up by the protest groups, has been handed over to the social services and the police.
Roger Ching from the city council said that people on the list, that the council were not aleady aware of, would be approached to see if they wanted to move.
"If they do not want to move, we can't force them to do so," he added.