Kyle and Caroline Brewerton, who moved from Auckland about six months ago, said embassy staff told them to "give it a few days and it'll settle down", The Dominion Post newspaper reported.
Mr Brewerton said while other embassies were organising evacuations, "you just get nothing out of ours".
"What happens if it doesn't all blow over...do we just hope for the best? Or do we have to see a couple of New Zealanders get hurt before anything happens?
"It would be good to see a bit of action."
Mr McCully defended the embassy's response, saying distressed people may not have most accurate inform.
"We need to understand that we are dealing with desperate and distressed people in some circumstances. The account I've had from the embassy is different from that and they maintain they have attempted to render substantial assistance to the family," he told NZPA.
The embassy had spent considerable time helping the family, he said.
Mr McCully said the ambassador in Cairo had made it very clear that "every reasonable assistance should be given to people who are caught up in this challenging situation".
The Ministry of Foreign Affairs said there were 295 New Zealanders registered in Egypt, and there were likely to be others who had not registered.
Ambassador Rene Wilson said only about nine New Zealanders were at Cairo airport earlier today and several were able to get out on commercial flights.
"Only a few are trying to leave through the airport at present. Of course if circumstances change and the political situation deteriorates considerably, then I would expect the numbers of those wishing to leave to increase rapidly," he told Radio New Zealand.
Mr McCully said the Government had not yet decided it was necessary to send a plane to Cairo.
"New Zealand taxpayers would not be very happy if the New Zealand Government sent an expensive aircraft at their expense and we loaded five people on board.
"There are a whole bunch of things that need to align before it becomes a sensible thing for us to do."
He said the Government was talking with other countries it usually cooperates with in such situations.
"But we are obviously to be prudent, and have been for some days looking at what aircraft availability of various types there might be should we need to follow that option up."
He repeated that the most immediate preference was for commercial flights, "simply because those are the most immediately accessible".
"The best advice we still have is that there are commercial flights available," he said.
"If there's a threat to the safety of New Zealanders and we have a significant demand for departures that can't be met commercially then obviously we want to be prepared and we have been working for some days to make sure we are prepared if that eventuality should occur."
Mr Wilson said the embassy was monitoring the situation closely.
"Things are relatively quiet today, but that's just today. Tomorrow there's a very big demonstration and we're uncertain about what the condition will be in the city tomorrow. The airport itself was pretty good today."
Asked if there was a need to move quickly as the demonstration loomed, Mr Wilson said "a lot of attention" was being given to the matter in Wellington.
Embassy staff were facing the difficulty of not having an office to work out of -- it has been damaged in the violence -- and has had communication issues as well, as network access remained sporadic.
The New Zealand embassy ground floor was damaged in protests over the weekend and was without power. Staff were working out of the ambassador's residence.
* For the latest travel advisories from the Ministry of Foreign Affairs and Trade on the situation in Egypt, see safetravel.govt.nz.
- NZPA
