The Department of Foreign Affairs says at least nine Irish people are believed to be among the 2,000 people stranded in Peru in the Machu Picchu region.
Rescue teams are only able to evacuate people via helicopter, as mudslides and torrential rain have left the road and rail tracks into the area impassable.
Priority is being given to elderly people.
Most of those stranded have been accommodated in hotels and none are said to be in any danger.
Peru scrambled helicopters to evacuate some 2,000 tourists stranded in after torrential rains and mudslides killed five people and cut off access to the ancient Inca citadel of Machu Picchu.
Tourists became trapped at the World Heritage site in the jungle in eastern Peru after the heaviest rains in the area in 15 years flooded the zone over the weekend.
An Argentine tourist and a Peruvian guide were killed along the trail in separate mudslides, the Peruvian government said, while two other deaths were reported over the weekend. The fifth person was killed when a hillside collapsed.
Prime Minister Javier Velasquez, who visited the area yesterday, said some 250 homes were washed away by the rains, as well as bridges and parts of several highways.
'The situation is chaotic,' Washington Farfan, a guide at Machu Picchu, told Reuters.
'Unfortunately, the rescue effort has not been organised correctly. People are really upset right now,' he added.
Machu Picchu, which was built in the mid-15th century and lies some 1,100km southeast of the country's capital Lima, is Peru's top tourist destination. About 500,000 people visit the site, which sits around 2,400m above sea-level, each year.
The government declared a state of emergency and the company that runs trains between the Inca ruins and the nearby city of Cusco suspended services.