"Police don't have the resources ... they can't get to burglaries on time, let alone beggars," he said.
However, he said the problem still remained: "Wellingtonians are too generous."
Wellington mayor Celia Wade-Brown echoed Mr Eagle's views, saying criminalising vulnerable people in the city wouldn't solve the problem.
"Begging is a symptom of wider issues -- lack of mental health services, people's addictions and lack of joined-up programmes when people are paroled from prison without housing options being sorted.
"It also detracts from the look and feel of the city," she said.
She said increasing housing supply, funding the city's night shelter to open in the daytime and encouraging people to contact health services, would start solving the issues.
However, local councillor Nicola Young said beggars should be banned from "lucrative areas" of the city.
Beggars are frequently seen near cash machines and convenience stores in Wellington's city centre.
"We need to freeze them out of very lucrative areas and away from the cash machines.
"People should stop giving money to beggars and instead give money to the downtown ministry or the night shelter," she said.
Ms Young said the city needed more facilities to prevent beggars on the streets.
"Beggars are there because they have psychiatric and addiction problems.
"We have been told some are just lonely. We need to increase council resources in core council roles."
Roi Reid frequently sits on Wellington's Manners St next to a convenience store and a cash machine, to ask for money.
The 37-year-old earns about $70-$150 a day from passers-by.
Mr Reid, who suffers from bipolar disorder and schizophrenia, lives in an apartment building in the city centre, paying $160 a week in rent.
He receives $270 a week from the Government.
He has sat on the streets of Wellington for four years, and said he hoped to get a "good paying job" by getting an education.
"I was thinking of joining the army to get a free education."
Mr Reid said if beggars were banned in the city, they would struggle to find a job.
Manners St City Stop convenience store owner Ab Patel said he didn't have a problem with beggars outside his business, as long as they keep away from the front door.
"They don't give us any kind of trouble but when they are drunk they throw glass bottles on the road outside."
He said the same few people sat outside every day asking for money.
"One would sit in the morning and then one comes later in the afternoon and then one at night."
He's only had two customers complain.
"It's not a personal thing but if they are sitting asking for money away from the door, it's fine," he said.
In 2013, a by-law was passed by Auckland Council banning beggars who were intimidating or causing a nuisance on the streets.
Auckland mayoral candidate David Hay said beggars needed support.
"Banning them from our streets would simply make their already desperate situations worse. It would be an act of incredible cruelty and heartlessness."
He said anyone who promoted the ban had "no understanding of, or empathy for, the plight of urban street-dwellers".
"Living on the street is, sadly, the best they can do. These people need our compassion and support."
Auckland City Mission acting chief executive Jacki Richardson said the number of homeless people has risen in Auckland CBD.
Last year 160 people were identified as being homeless in Auckland CBD in a street count conducted in a three-kilometre radius around the Sky Tower.
Three years ago 68 people were seen as being homeless in the same area.
Ms Richardson said the numbers were "certainly significant", however, new developments in the city may have contributed to it.
"People are much more obvious now than they were before.
"There used to be a lot of empty buildings in the city and it was quite easy for a homeless person to cover and take shelter.
"But now there's cranes and buildings turning into apartments so there's not that much space for them to set themselves up at night," she said.
Wellington begging recommended options
* The street outreach team continue to engage with beggars with increased emphasis on connecting them to services.
* Respond to complaints about beggars consistently.
* Advise beggars on keeping footpaths clear.
Other options
* Council could consider the possibility of introducing a by-law that bans citizens from giving to people who beg.
* Regulate when and where people can beg. Anyone found begging without a valid permit could have their permits revoked.
This option isn't recommended.
Auckland public safety and nuisance by-law
• Came into effect May 2013.
• A person must not use a public place to: beg, in a manner that may intimidate or cause a nuisance to any person; wash or offer to wash a vehicle or any part thereof, in a manner that may be unsafe or intimidate or cause a nuisance, or cause an obstruction to traffic; create a nuisance through the use of playing of any instrument (musical or otherwise), any type of public address system or any type of amplified sound system, or by making any excessive sound or noise.
• Nuisance is defined as: a person, animal or thing or circumstance causing unreasonable interference with the peace, comfort or convenience of another person whether or not that person is in a public place.
