At least one employee had left her job in the area because of the problem, they said.
Nash was on other duties in Napier at the time the petition was delivered to his Tennyson St office and Dalton was in Auckland but both said later similar problems exist in many communities around the country, but don't just relate to policing.
Nash said it's among the reasons the new Labour-led coalition Government has moved to create 1800 more police jobs and also review mental health services, including hopes of improving accommodation and care options away from civic attractions such as squares, gardens and other public facilities.
He said he sympathises with the businesses now being hit with problems which escalated because of the previous Government's slow response to synthetic drug retailing, loss of huge numbers of state housing units, and deterioration of mental health services and facilities which are "not fit for purpose".
"I share their concern," he said. "It is a real issue, and when you've got professional businesspeople whose clients don't feel safe you have a real problem."
He said it would be "cold comfort" that the Government is aware there are people who need "supported living", because it will take time to get the funding and options sorted, among other priorities.
Dalton said illegal activity is a matter for police, but the street problems in and around the CBD and in the squares included a lot of activity which was not illegal.
"I am fully aware of the problem," he said. "We've done everything we can, but we are very concerned. It is an issue.
"It's not a good look for Napier," he said, "but every city has the same problems. Every city in the country is grappling with it."
The council had provided security staff in the CBD and surrounds and while it has no immediate plans for developments in the vicinity of the square it is considering options for resiting the Napier Public Library nearby, which he said would enhance the environment.