Richard Dicker, director of HRW's international justice programme, said: "The execution of these two, however heinous the crimes involved, is cruel and inhuman punishment that will only drag a deeply flawed process into even greater disrepute."
"The tribunal repeatedly showed its disregard for the fundamental due process rights of all of the defendants."
The statement by HRW comes days after Louise Arbour, the United Nations high commissioner for human rights, also appealed to Iraq not to execute Barzan and al-Bandar.
Swift execution urged
However, Abdel Aziz al-Hakim, Shia leader of the Supreme Council of Islamic Revolution in Iraq (SCIRI), on Monday called for a swift execution of the two former aides.
"We demand in the name of the Iraqi people that the prime minister and the government accelerate the carrying out of the execution of those criminals who have been sentenced."
He also urged authorities to "stay on course to take legal actions against the others to achieve justice."
A video of Saddam's execution, filmed on a mobile phone and released over the internet, showed Saddam being taunted on the gallows, in contrast to an official video that was released without sound.
"The execution of Saddam Husseim is an outrageous act against humanity"
Avicena, Zaragoza, Spain
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Dicker said: "The haste and vengeance infusing Saddam Hussein's hanging should prompt the Iraqi government to halt these [upcoming] executions."
The internet video provoked an outcry around the world, with many international leaders saying the video showed the execution to be closer to a sectarian lynching than a court-directed punishment.
But Nuri al-Maliki, the Iraqi prime minister, has defended the execution and said that Iraq might "review" relations with countries that criticised the hanging.
"The execution of the tyrant was not a political decision, as the enemies of the Iraqi people say.
"The verdict was implemented after a fair and transparent trial, which the dictator never deserved," al-Maliki said on Saturday.
HRW has said the execution obscured Saddam's "unspeakable human rights record" and raised questions about the new government's "commitment to fundamental human rights".