Newport council said it had consulted on the plans at a time when efforts were being made to improve the area, including building a shopping centre.
It said the issues were among the most frequent concerns reported to Gwent Police and the fire service.
But human rights organisation Liberty said a ban would "criminalise the most vulnerable in the city".
The organisation has written to council leader Bob Bright to express its concerns.
Rosie Brighouse, legal officer for Liberty, said: "These proposals make a mockery of Newport's Chartist legacy."
The council wants to introduce a new Public Spaces Protection Order to tackle anti-social behaviour ahead of the opening of the new Friar's Walk shopping centre next month.
It has consulted with members of the public about what they would like to see included, such as a ban on begging, rough sleeping, dogs who are not on leads and leafleting in the city centre.
Councillor Bob Poole, cabinet member for regulatory functions, said the council was trying to make the city centre a more appealing place to visit.
"Few people in Newport will have failed to notice the changes taking place in the heart of the city centre, most notably Friar's Walk retail development due to open in November and arguably the most significant investment in Newport's recent history," he said.
"It is perhaps timely, against this background of positive change, that this new piece of legislation offers the city and its residents the chance to build on that momentum by ensuring that the experience of people visiting the city centre is a positive one."
The council has so far received 350 responses to the consultation and said all views would be taken into consideration before a final decision was made.
It added it was committed to helping homeless people and was working with other services to address the "underlying needs of those affected in this way".
The proposals will be discussed by the council's scrutiny committee on 15 October.
Begging and rough sleeping could be banned in Newport city centre in a bid to make the area more appealing.