The rescue operation in the Machu Picchu area of Peru is expected to take a number of days as helicopters are the only way of getting to those who have been left stranded by the torrential rain and mudslides.
At least nine Irish people are thought to have been among the thousands of tourists left cut off in the region.
There have been no reports of any Irish casualties.
Peruvian helicopters have already airlifted some 600 tourists.
'We have evacuated 600 tourists, but there are still almost 1,500 at Machu Picchu,' Peruvian Prime Minister Javier Velasquez told reporters.
About a dozen helicopters were used in the unprecedented airlift 'but the persistent rains in the Cusco region are delaying the operation,' he added.
The railway line that transports tourists between Aguas Calientes, at the foot of the ruins, and the city of Cusco, the ancient Inca capital, has been damaged and the tracks remain broken.
Hundreds are still said to be stranded in Aguas Calientes with scores more believed trapped on the Inca Trail, a narrow Andean pathway up to Machu Picchu that takes four days to complete.
With the trail already cut in several places by landslides, there are fears for the remaining backpackers on the trek.
A 23-year-old Argentine tourist and a 33-year-old Peruvian mountain guide died on the trail, buried under mudslides, the National Culture Institute in Cusco said.
The other fatalities occurred along the valley leading to Cusco and in the town itself.
But Mr Velasquez rejected accusations that the government was giving priority to foreign tourists and that some were bribing their way out. He said people over 60, children and the sick were the first to be evacuated.
The Peruvian government has also sent food aid to the 8,000 residents of Aguas Calientes, cut off by landslides and swollen rivers.
Officials defended the slow pace of the operations, saying they were being hampered by the heaviest rains in 15 years.
