The father of a missing two-year-old has made a desperate plea to her would-be abductor, during an emotional press conference today.

Allan Symes thanked the people of west Auckland for their dedicated support as the search for Aisling Symes continued into its fourth day.

"Aisling is our two-year-old daughter, sister to Caitlin, cousin and beloved niece and granddaughter. We want her back so please if you have any information, any at all, please come forward," Mr Symes said.

Parents grief stricken

He described the last four days as "the most harrowing of our lives".

"No sleep, it's been like we're barely existing, surviving every moment not knowing where Aisling is. Is she near us? Is she being treated well? Things like, has her nappy been changed?"

Allan was joined by his wife Angela and Inspector Gary Davey, who said police empathised with the family but don't have a lot to add.

He said the investigation had been increased to over 40 officers and he was looking to increase that again this afternoon.

Public appeal for help

"I'm appealing to anyone with information, no matter how trivial, that it is important to come forward," Mr Davey said.

"To whoever has Aisling out there, the sole focus of police at the moment is to have Aisling returned safely.

"We hope you come forward and leave her in a safe place where she can be found."

Mr Davey said the Commissioner of Police, Howard Broad, had visited the Henderson Police Station and met with the Symes family today.

He was asked about a possible reward being offered but said it was not necessary given the level of support from the public.

"Police are looking at not just persons of interest but behaviour of interest," Mr Davey said.

"We have identified people in the area through the area canvas and local intelligence and what we're doing is profiling people of concern."

Mr Davey said police had received a number of calls from the public about potential sightings of Aisling but at this stage none had panned out.

Following the press conference Angela and Allan left the room before Angela was heard bursting into tears outside.

Earlier both parents told nzherald.co.nz they were not concerned with whoever had their daughter - they just wanted her returned safe and well.

Angela Symes cried as she said: "Just as long as they are looking after her."

Aunt's plea

The toddler's aunt Aithne Potts urged anyone with information to come forward or just drop Aisling off somewhere safe.

"As long as she's safe and well we don't give a damn [about who took her]."

Police searching for Aisling are now looking at any reports of suspicious behaviour in the Henderson area in the past few weeks, particularly involving child-related offending.

TV3 this morning reported that police were going to an address in Henderson after a possible sighting of Aisling, but the story was later taken off their website.

As the search for the 2-year-old intensified yesterday, police confirmed they believed she had been abducted.

Aisling's disappearance

Aisling disappeared about 5pm on Monday from her deceased grandparents' vacant Longburn Rd home, which her mother, Angela Symes, was cleaning.

Earlier, neighbour Cherie Tahitahi had heard Aisling and her sister, Caitlin, 5, giggling at some ducklings.

Mr Davey said it was unlikely Aisling had been swept out to sea and police believed she could be with a stranger.

Suspicious behaviour had been reported in the area recently, he said, but he would not say whether that involved paedophiles.

"We will be profiling people of interest who were either predisposed to that type of behaviour or living in the area."

Yesterday, police went door-knocking. They want people to report any suspicious behaviour within 5km of Longburn Rd.

Mystery Woman

Early this week, police said an Asian woman had been seen talking to Aisling just before her disappearance. The woman was in her 30s, about 165cm tall with a medium build and long straight black hair.

She was wearing a black crew-neck top, with three-quarter-length sleeves, three-quarter-length blue jeans and black leather sandals and black socks.

She had a black and grey medium-sized dog on a lead.

"Someone will know who that Asian lady is with the dog and whether there have been sightings of an Asian woman in and around that Longburn Rd area," Mr Davey said.

Police were confident Aisling was not in the area so had to look at the abduction scenario, "given her age and the possibility of how far she would move under her own steam".

Last night, ESR forensic staff were seen in the Longburn Rd house. Mr Davey said they were doing a forensic search as part of "standard policing procedures".

"Police have to keep an open mind as far as all possibilities, whether she's gone missing through misadventure or has been abducted. I think it would be remiss if we didn't keep all avenues open," he said.

Aisling a 'bubbly little toddler'

Aisling was yesterday described as a bubbly little toddler who loved to play with people and animals.

Her name, derived from her Irish father Alan's side of the family, means "vision of heaven". And by all accounts, this is appropriate.

Her devastated family fear the toddler's outgoing nature made her easy to snatch.

"She didn't have any inhibitions that I could see," her uncle David Ball said from the family's Massey home.

Ms Potts said the toddler had no qualms about being with large groups of people - be they family, friends or church members.

Mr Ball said Alan and Angela Symes were with police yesterday "trying to get the big picture and sort everything out".

Mr Symes, as a former search and rescue worker and security guard, had been taking a keen interest in the efforts to find his daughter.

But after an extensive, fruitless search of the 3km area surrounding the house - by land, water and air - police suspended it.

But Ms Potts described her niece as a typical, happy little girl who loved music, dancing and playing with animals and her dolls.

"She was a maternal little girl who would dress her dollies up and put them to bed."

Aisling's vocabulary was limited, but as a passionate eater, she could name quite a few foods.

"Strawberries, tomatoes ... cheese is another favourite. She will happily say 'cheese'. I think if given half a chance she would empty the fridge of cheese."

On behalf of the family, Ms Potts pleaded for the toddler's safe return.

"We don't understand why it's been so long and we know nothing, so please tell us where she is. We just want her home."

* Police are urging anyone with information to phone 0800 4 AISLING or call into a special police point in the Lincoln North Mall on Lincoln Rd.

Police ask that people ringing the 0800 number do not suggest checking the dog registers. They say this is useful advice but has already been carried out.