Last month the commission narrowly voted down a United States-sponsored resolution condemning Cuba for abuses of human rights.
This undercuts Washington's image as a champion of human rights, they say, after many Presidents have condemned Cuba and other Communist nations for denying the right to emigrate.
The vote on the measure, which refrained from condemning Cuba outright, was 23 to 21, with nine countries in the 53-member commission abstaining.
While not explicitly condemning Cuba, several of the dignitaries expressed carefully worded support for the dissidents' concerns.
The dispute started with Argentina's vote to condemn Cuba over human rights at the meeting of the United Nations Human Rights Commission in Geneva.
A last-minute ploy by China tonight held up a Security Council statement condemning Cuba for its attack on civilian aircraft.
The United States also failed to get support for a vote condemning Cuba in as strong terms as Washington wanted.
I therefore deeply regret the fact that I must on this occasion most vigorously condemn Cuba, and I would call upon that country immediately to release all the detainees.
"We are not condemning Cuba," he said.