Cuban President Raul Castro demanded an end to the US embargo on the island, which he considers "the chief obstacle to the economic development" of his country.
In his speech at the UN, Castro said the renewal of diplomatic ties between Cuba and the US plus the changes decreed by US President Barack Obama "constitute an important step forward", reported Efe news agency.
"The economic, trade and financial blockade against Cuba has continued for over half a century," he said in his speech at the Sustainable Development Summit being held at the UN.
According to Castro, the embargo "causes harm to the Cuban people", affects other nations and also hurts American companies and citizens.
Cuba, for more than 20 years, is urging the UN General Assembly to pass a resolution critical of the embargo, a text that normally obtains majority backing, but which, for the first time could pass without a US vote against it.
According to Cuba, since the US embargo was implemented in 1962, it has cost the island a total of $833.7 billion.
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The Cuban president, who was greeted with enthusiastic applause by participants at the summit, slammed the "unacceptable levels of poverty" in many parts of the world, the growing economic gap between north and south, and the increasing "polarisation of wealth".
He said the development achieved in the 15 years of the Millennium Goals has been "insufficient" and its rewards have been "unequally distributed".
Following his speech on Saturday, Castro will speak at the General Assembly on Monday, when Obama will also be present.