A man has appeared in court today charged with the abduction of a seven-year-old girl, and sexual violation and assault with intent to commit sexual violation, police say.

The man, who was arrested in Cheviot, North Canterbury, about midday yesterday by members of the armed offenders, was given name suppression and returned to police custody.

Police had been searching for him since the disappearance of 27-year-old Vanessa Pickering and her daughter who were last seen on Monday evening at their New Brighton home.

At the time the man was wanted by police in relation to a sexual assault on Monday.

Ms Pickering's daughter was found by a member of the public on her own in a paddock near Kaiapoi on Tuesday morning.

The girl was able to give police some information, Detective Senior Sergeant Virginia Le Bas said.

As each day passes the concern for Ms Pickering's safety and whereabouts has increased, Ms Le Bas said.

"She's had no contact with her family or friends."

The police and Ms Pickering's family has asked anyone who might have information about where the missing woman was to contact police.

"We are still interested in any sightings of the vehicle - a blue/green Toyota Estima, EFA 478 - in and around the Canterbury area over the past week," Ms Le Bas said. They were particularly keen to hear of any sightings of it in the north Canterbury area from Monday until noon yesterday when it was located by police.

Police and Land SAR volunteers will continue their search for Ms Pickering today, starting at Godley Head.

"A large area was searched yesterday with no clues to establish where Vanessa is," Ms Le Bas said. "Many people have been spoken to by police to establish what exactly has happened to Vanessa but we still need more information."

Meanwhile, a page dedicated to finding Ms Pickering has been set up on social networking site Facebook.

So far 132 people have joined the site and many have written messages of support for Ms Pickering and her daughter.