"We got really scared and turned around right away. We were even too scared to look around and see if he was pointing it at us," the tourists told the Herald.
They said it was their last day in New Zealand and it was a frightening way to farewell the city.
Armed police near Federal St near the Sky Tower.
A police spokesman said police received a report from a member of the public relating to an individual who they reported as possibly having a firearm.
"Police are currently making inquiries to establish what has occurred.
"Staff are currently armed, as is standard procedure in responding to jobs of this nature," he said.
Another witness said he saw a couple of officers speaking to the two female tourists and then all of a sudden a couple of police officers jumped in a car and took off.
"Armed police had been circling the area since about 3.30pm," he said.
