The death penalty is common across the Caribbean, as are laws against cross-dressing and gay sex.
The government said officials also plan to meet with leaders from Christian, Hindu and Islamic communities who represent Guyana's most prominent religions. Many religious leaders in the country oppose legalization of homosexuality.
The independent Society Against Sexual Orientation and Discrimination said it will campaign to remove what it says are extremely discriminatory colonial-era laws.
"It is making criminals out of ordinary people," spokesman Joel Simpson said, noting that under current law, two consenting male adults could face a minimum of two years in prison for having sex in the privacy of their home.
Many Guyanese are opposed to the discussions because they want the current laws to remain untouched.
Rayon Griffith, a food vendor in the capital of Georgetown, said he already worries about gay and lesbian displays of affection on TV.
"I am worried that a whole generation is coming up thinking this is right," he said.
Others are opposed to abolishing the death penalty.
"We have a nation with criminals with warped minds," said Cranon Henry, a 41-year-old security guard. "Hanging will make criminals fear attacking people. Once they kill two or three of them, you will see how quickly the murder rate will go down."
National Security Minister Clement Rohee already has launched the debate on hangings via televised panel discussions that last up to one hour and allow for call ins. People also will be able to attend town halls on the issue later this month. No one has been hanged in Guyana since 1997 even though the law remains on the books. Nearly 30 prisoners are on death row.
Teixeira said the government will inform the U.N. in October about the results of the discussions even if they are still in progress.
"We are keeping our promise to consult with an open mind," she said.