Standards of justice
In a statement, the group acknowledged the Singaporean government’s right to punish any person within its territorial jurisdiction for any act constituted as an offence in Singapore.
It insisted, however that international standards of justice and due process of law be observed.
The group's statement did not details the alleged "irregularities".
Also convicted and on death row in the same case is Okeke Nelson Malachy, 35, a stateless African.
Malachy was arrested after his picture was shown to Iwuchukwu, who identified him as the person to whom he was supposed to deliver the drugs.
It is not clear whether Malachy's clemency appeal had also been rejected.
Drug laws
Singapore has some of the world's harshest drug laws, including a mandatory death penalty for anyone found guilty of trafficking more than two grams of heroin.
Amnesty International, the human rights group, has said Singapore has the world's highest per capita execution rate.
A letter from Singapore's Prisons Department informed Iwuchukwu's family of the execution and said the department would allow him extra visits in the three days before he is executed.
His family lives in Nigeria.