Bruno Rodriguez, Cuba's foreign minister, said in his speech before the assembly that the embargo had cost the island's fragile economy tens of billions of dollars during its 47-year duration and that it had prevented Cuban children from receiving medical care.
"The blockade is an uncultured act of arrogance," Rodriguez said, adding that the policy was an "an act of genocide" that is "ethically unacceptable".
"President Obama has a historical opportunity to lead a change of policy toward Cuba and the lifting of the blockade"
Bruno Rodriguez, Cuba's foreign minister
The General Aseembly held the annual vote for the forst time since Barack Obama, the US president, took office in January and pledged to improve relations with countries that Washington has long been in opposition to.
The Obama administration has relaxed finance and travel restrictions on US citizens who have relatives in Cuba, and sent a diplomat to Havana in September in what was called the most senior-level talks between the US and Cuba in years.
However, Washington has said that Cuba must still make several economic, political and financial changes before it will consider lifting the embargo.
"President Obama has a historical opportunity to lead a change of policy toward Cuba and the lifting of the blockade," Rodriguez said.
He said that "there has not been any change in the implementation of the economic, commercial and financial blockade against Cuba" since Obama's inauguration.
Susan Rice, the US ambassador to the UN, responded by calling Rodriguez's comments "hostile" and "straight out of the Cold War era", and said that the Obama administration remained committed to engaging with the Cuban government.
"The United States has demonstrated that we are prepared to engage the government of Cuba on issues that effect the security and well-being of both our peoples," Rice said during her speech to the assembly.
But several respesentatives spoke against the embargo, calling it an affront to international law and that it had hurt ordinary Cubans rather than the country's government.