His daughter, Lorraine Cook, gathered with other family members at the Hamilton East house her father shared with her mother, reported Fairfax.
She said Ataahua, whom Mr Morgan has had since he was a puppy, kept escaping from the home to sit at the river.
"When we were told my dad had gone missing, my brother and sister were here at the house, waiting for news from police, before we all turned up.
"They let Ataahua out of the house to go toilet. About 11pm that night, they had to go looking for her.
"One of the cops and my brother found her down by the river again in the same place, just sitting there. It was like she was waiting for him to come back.
"She keeps trying to run down there - it's sad to watch her. She looks sad."
Senior Sergeant Robbie Hermann of Waikato police said Mr Morgan often stopped at an area about 100m north of the Wellington St beach "and sometimes sits in the shallows of the river while his dog has a swim".
Police have described Mr Morgan as European, about 1.8m tall and thin.
His shoulder-length hair is brown and grey.Anyone with information about his whereabouts is urged to call Hamilton police on (07) 858-6200.
