Peru had demanded that Yale return the historical treasures, which include mummies, ceramics and human bones excavated by Hiram Bingham, the explorer, between 1911 and 1916.
Yale administrators said they offered a deal that would have transferred ownership of some of the artefacts to Peru for display at a new museum. A parallel exhibit would have remained at Yale University in New Haven.
In a statement released on Wednesday, the college said: "We are disappointed that the government has rejected this proposal and is apparently determined to sue Yale University."
Eduardo Ferrero, Peru's ambassador to the United States, dismissed the university's deal, saying that Yale officials attempted to "characterise their proposal as an equitable joint division of artefacts for two museums".
Ferrero said that Yale still refused to acknowledge Peru's ownership of the artefacts and "proposed that these artefacts belong to humanity, and at the same time pretended to keep part of the collection".
He said that while Bingham received approval to remove the artefacts, that approval was conditioned on Yale recognising Peru's legal ownership and the understanding that "the artefacts were on temporary loan and would be returned to Peru".
Highly organised society
Even under Yale's proposed deal, he said, the artefacts would not be returned until Peru builds a new museum, something for which funds have not yet even been raised.
Ferrero said: "The government of Peru is surprised by the position taken by the authorities of such a prestigious university and will soon present a lawsuit in US courts against Yale University."
The Incas ruled Peru from the 1430s until the arrival of the Spaniards in 1532, constructing stone-block cities and roads and developing a highly organised society that extended from modern-day Colombia to Chile.
The ruins at Machu Picchu, on a mountaintop above a valley 500km southeast of Lima, are Peru's biggest tourist attraction.
Bingham, an archaeologist with Yale, became the first foreigner to reach Machu Picchu in 1911 and returned to the site in 1912 and 1914. Yale said artefacts from the 1914 expedition were returned long ago and said the current dispute focuses on relics from the 1912 trip.
Many of the artefacts are on display at Yale's Peabody Museum.