The seven were spotted by a New Zealand air force Orion patrol plane as they floated in the open sea about 300 kilometers (186 miles) southeast of Nauru island, said Sandra Ford, spokeswoman of the New Zealand Rescue Coordination Center.
The plane directed a nearby fishing vessel to pick up the survivors, she said.
The seven were among 50 people aboard the inter-island ferry MV Butiraoi, which left the island of Nonouti in Kiribati on January 18, bound for Betio in the Kiribati capital of South Tarawa, according to the release.
Ford said the survivors included three adult females, a 14-year-old girl, and three adult males. The oldest of the group was 34, she said.
A search will continue for other survivors, she said, with aircraft returning at first light Monday, and the fishing vessel, the FV Lomalo, to stay on station overnight.
Ford described the area where the dinghy was found as “quite remote,” and said other ships would take at least 24 hours to get there.
The ferry MV Butiraoi was on a 250-kilometer (155-mile) trip that was expected to take two days, according to New Zealand authorities.
When the 17-meter-long (56 feet) catamaran-style passenger ferry didn’t arrive in Betio on January 20, the search began.
Ford said authorities were still trying to determine when the ferry sank, but she said it was thought to be early in its journey.
New Zealand’s Rescue Coordination Center has been in charge of the search since Saturday, taking over from authorities in Fiji.
New Zealand is about 4,500 kilometers (3,425 miles) south of Kiribati.