The extremely rare book, which dates back to 1494, is being auctioned by Nate D. Sanders Auction on their website and could fetch as much as £600,000.
Anyone wanting to get their hands on the rare book will need to raise more than $750,000 (£590,000), the current highest bid, with the online auction ending tonight.
In the historic letter Columbus said the new lands he discovered justified the expensive and risky expedition.
A Spanish version of the letter was printed in Barcelona in early April 1493 and a Latin translation was published in Rome around a month later.Christopher Columbus, depicted around 1592, set out for the East Indies in 1492 but instead stumbled upon the Caribbean islands of the Americas
The Latin version was swiftly disseminated and reprinted in many other locations. Leander de Cosco translated the letter into Latin for this 1494 Basel edition.
Six woodcut prints designed by German artist Albrecht Durer which represent the first depictions of the new world are also included in the hardbound book.
They show the arrival of the Spanish at the island Insula Hyspana, a map of the Antilles, the construction of the fort La Navidad on the island of Hispaniola and Columbus' caravel under full sail.
Woodcuts were an ancient technique in printmaking where an artist carves an image into the surface of a block of wood.
The book belongs to the Robert Menzies collection, the personal library of former Australian Prime Minister Sir Robert Gordon Menzies.
A spokesman for US-based Nate D Sanders said: 'The book is significant because it is Columbus' account of discovering the new world, which he wrote on the Nina while sailing back to Spain.
'According to the Library of Congress, 17 editions of the letter were published between 1493 and 1497 and only eight copies of all the editions still exist.'
Columbus set out on his first voyage in August 1492 with the objective of reaching the East Indies by sailing west across the Atlantic Ocean.
Instead of reaching Asia, Columbus stumbled upon the Caribbean islands of the Americas.
Convinced he had discovered the edges of Asia, Columbus set sail back to Spain.
The letter that launched a thousand ships: Columbus' letter telling of the new world
'To the first island I discovered I gave the name of San Salvador, in commemoration of His Divine Majesty, who has wonderfully granted all this. The Indians call it Guanaham.
'The second I named the Island of Santa Maria de Concepcion; the third, Fernandina; the fourth, Isabella; the fifth, Juana; and thus to each one I gave a new name.
'When I came to Juana, I followed the coast of that isle toward the west, and found it so extensive that I thought it might be the mainland, the province of Cathay.
'I heard from other Indians I had already taken that this land was an island, and thus followed the eastern coast for one hundred and seven leagues, until I came to the end of it.
'From that point I saw another isle to the eastward, at 18 leagues' distance, to which I gave the name of Hispaniola.
'There are many spices and vast mines of gold and other metals in this island.
'They have no iron, nor steel, nor weapons, nor are they fit for them, because although they are well-made men of commanding stature, they appear extraordinarily timid.
'The only arms they have are sticks of cane, cut when in seed, with a sharpened stick at the end, and they are afraid to use these.
'Often I have sent two or three men ashore to some town to converse with them, and the natives came out in great numbers, and as soon as they saw our men arrive, fled without a moment's delay although I protected them from all injury.
'At every point where I landed, and succeeded in talking to them, I gave them some of everything I had-cloth and many other things-without receiving anything in return, but they are a hopelessly timid people.
'It is true that since they have gained more confidence and are losing this fear, they are so unsuspicious and so generous with what they possess, that no one who had not seen it would believe it.
'They never refuse anything that is asked for.
'They even offer it themselves, and show so much love that they would give their very hearts.
'Whether it be anything of great or small value, with any trifle of whatever kind, they are satisfied.
'I forbade worthless things being given to them, such as bits of broken bowls, pieces of glass, and old straps, although they were as much pleased to get them as if they were the finest jewels in the world.
'As for monsters, I have found no trace of them except at the point in the second isle as one enters the Indies, which is inhabited by a people considered in all the isles as most ferocious, who eat human flesh.