MFAT continued attempts to establish and maintain contact with them.
The British Embassy and Peruvian authorities had been given a list of New Zealanders affected and the embassy would assist wherever possible, MFAT said.
About 700-800 people had been evacuated today and the same was expected tomorrow -- weather depending.
Peruvian authorities were expected to update MFAT tomorrow about the New Zealanders' evacuation.
MFAT advised anyone travelling to Peru to register their details with MFAT.
Families with serious concerns about relatives should call (04) 439 8000.
About 2000 people were initially trapped. This remained at about 1600 tourists as more travellers trickled in each day, Peru's Foreign Minister Jose Antonio Garcia Belaunde told The Associated Press.
Machu Picchu is one of the most popular destinations for tourists in Latin America, attracting more than 400,000 visitors a year.
The 15th-century Inca fortress is located on a high mountain ridge. A railway that transports tourists to the site was covered by a mudslide.
The country's civil defence service estimated the homes of 1300 people in poor rural areas - many of them riverside dwellings made of clay and straw - were destroyed, while many others were damaged.
Food and other aid was being transported in for those left homeless.
- NZPA