Argentine diplomats handed 800kg (1,760 lbs) of documents to the UN, saying it was the fruit of 11 years of research.
The 1,700,000 sq km (650,000 sq miles) includes the Falkland Islands and the islands of Georgia and Sandwich.
Argentina has been in dispute with Britain over the sovereignty of the islands for more than 170 years.
The claim adds to the 4,800,000 sq km of continental shelf spreading out 320 km (200 miles) from Argentina's coast.
It has also been in dispute with Chile over parts of Antarctica which are also included in the claim.
Detailed research
The Argentine documents handed in to UN diplomats in New York included scientific measurements of the depth of the sea around the Argentine coastline.
What the documents are trying to prove is the extent of the continental shelf way out into the ocean.
This is significant, as under current international legislation, a state's ownership of the continental shelf can exceed 200 nautical miles until its natural extension ends.
Argentine Foreign Minister Jorge Taiana said the documents were the culmination of 11 years of research and diplomatic effort to prove the size of Argentina´s sovereign territory.
He also said that if the United Kingdom wished to present its own claim to the continental platform around the disputed Falkland islands - or Malvinas islands, as they are known locally - Argentina would object formally.
An Argentine foreign ministry statement said Great Britain had usurped the islands in 1833, illegally occupying Argentine territory, and that Britain had ignored calls by the UN to begin discussions over the issue.
