Talk of oil in the South Atlantic pre-dates the 1982 conflict. The economic zone for fisheries also applies to offshore mineral exploration.
But the search – which only began in earnest in 1995 - is still "in its infancy", says the government.
Six wells were drilled in 1998, two by Shell. They were said to prove there was potential for both gas and oil, but no commercial discoveries were made.
After analysis it is now believed drilling could succeed elsewhere in the basin.