Cuba has withdrawn a resolution calling on the United Nations' Human Rights Commission (UNCHR) to investigate conditions at Guantanamo Bay.
Hundreds of suspects are being held at Guantanamo Bay
The draft resolution, without naming the US, warned prisoners' rights in the US detention centre were being abused.
A BBC correspondent at the UNCHR meeting in Geneva said the Cubans felt there was too much American lobbying to guarantee passing the resolution.
At least 600 prisoners from the "war on terror" are being held at Guantanamo.
The US government says the suspects are beyond the jurisdiction of American law because they are held on foreign soil.
The American detention centre - known as Camp Delta - is built on territory leased by the US from Cuba.
Cuba tabled the resolution in mid-April, a day after the US sponsored a motion at the UNHCR criticising Cuba's human rights record.
The BBC's Elizabeth Blunt in Geneva says the Cuban motion eschewed typical rhetorical flourishes in favour of simple, skilfully worded language.
Its terms reminded countries of statements they had made in the past expressing concern over the detention centre.
This would have put many European states in a very difficult position.
They would have had to choose between the diplomatic embarrassment of backing Cuba against the US, or they would have had to contradict earlier statements by opposing the Cuban resolution.
The German representative on the UNCHR thanked the Cubans for dropping the resolution.
The BBC's Geneva correspondent says criticism of the US treatment of detainees in Guantanamo Bay is thought to have contributed to outspoken Irish politician Mary Robinson losing her job as UN High Commissioner for human rights.
The subject has been largely kept off the agenda at this year's commission session.