"Her family member is coming out - obviously, they're distraught. They're on the other side of the world and they haven't heard from her."
Beard said there was no evidence of foul play at this stage and police were speaking with people at the backpackers Millane was staying at - including those she was with on Saturday night.
He would not confirm what was left at the room, but said her belongings remained there.
It has since been revealed that Grace Millane, who has been in New Zealand for about two weeks, is the daughter of a millionaire property developer, David Millane, the Daily Mail reported.
His wife, Gillian, is recovering from an operation and will stay back in the UK, the newspaper reported.
Grace Millane, who graduated from the UK's University of Lincoln this year, reportedly saved for her trip to New Zealand by working at her father's company.
A talented artist, Millane has shared a number of her works - watercolour pieces - on a dedicated Facebook and Instagram page.
"Hope you are okay. Your friends and family are looking for you x please contact them if you can so they know you are ok. sending all my love to you.'' [sic]
Another has written: "Hey lady! Where are you? Everyone is worried. Please make contact with your friends and family.''
Millane's brother, Michael Millane, posted on social media that the family had been calling his sister's cell phone - but that it was going straight to voicemail.
He said she had been staying at X Backpackers - which she described as a "party hostel'' - and had been sharing a room with two other girls and a boy.
"She spoke to someone in the family every day on WhatsApp, Facebook or FaceTime. The contact with us stopped on Thursday.
"The last contact she had was with her roommate on Saturday morning.
"Her disappearance was completely out of the blue."