Agents say travellers have been asking about swapping but most have decided to stay with booked flights.
An international sports team due to fly to France on Malaysia Airlines is changing carriers because the players fear for their safety after the MH17 tragedy.
Flight Centre says about 100 customers have cancelled or postponed flights with Malaysia Airlines since its passenger jet was shot down over Ukraine last week.
The Samoa women's rugby team was due to fly to the Women's Rugby World Cup in France from Auckland on Saturday. But Samoa Rugby Union spokeswoman Rula Su'a Vaai said concerns were raised with the International Rugby Board, which advised that Malaysia Airlines would refund the cost of the flights.
The team was changing airlines because of "natural fear" after the airline was involved in the MH17 and MH370 tragedies, she said.
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A source close to the team said the players had raised concerns about flying with the airline after MH17 crashed on Thursday. Team management had passed their worries on to the Samoa Rugby Union and the IRB.
The source had been told flights for the 26 players and six management personnel would be rebooked with either Cathay Pacific or Thai Airways.
Samoa's preparations for the women's world cup were being done in New Zealand because the team had a mix of overseas-based players including a number who lived in New Zealand.
Meanwhile, New Zealand travel agencies continue to receive inquiries from customers concerned about travelling with Malaysia Airlines. However hefty rebooking costs mean most travellers are sticking with original bookings. Shortly after MH17 was shot down, Malaysia's national carrier told customers it would refund or postpone any flights booked from July 18 to December 31, 2014, provided the changes were made by tomorrow.
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Flight Centre said about 100 of its Malaysia Airlines customers had sought a refund for their airfares or made adjustments to travel bookings. General manager Simon McKearney said this was a relatively low number and he did not expect the MH17 tragedy to have a big impact on the number of Kiwis travelling internationally.
Harvey World Travel said few of its Malaysia Airlines customers had cancelled or postponed.
House of Travel commercial director Brent Thomas said retail outlets had had inquiries in the "tens rather than hundreds" over Malaysia Airlines, but few had changed or cancelled flights. Mondo Travel marketing manager Gordon Bayne said the agency had received inquiries from bargain-hunters about cheap flights. Malaysia Airlines said it was grateful for the support of travel agents and passengers. Lee Poh Kait, regional senior vice-president, said Australasia was the airline's main market outside Malaysia and it was determined to rebuild trust.