Sergeant Tony Woodbridge, of Oamaru, said a police communications centre was called by the American group about 3pm on Wednesday on an overseas cellphone.
They said they were lost on a track, stuck in mud, in the Waitaki Plains area and needed help. Police searched for the group for about 90 minutes before the search was called off after a centre staff member was able to reconnect with the caller.
Usually, police could use cellphone towers to get co-ordinates on cellphones, but the make of this phone made it difficult to get a fix on the location, he said.
By the time the staff member had contact with the tourists, they were "long gone" from the scene.
People should contact police if they found their way to safety on their own, he said, so searches could be called off.
