The American administration in Baghdad has sparked a diplomatic row with Prime Minister al-Maliki of Iraq by refusing to hand over for execution three war criminals convicted of genocide, including a cousin of Saddam Hussein’s known as “Chemical” Ali.

The dispute is threatening to sour relations between the Iraqi government and Washington and might even lead to the toppling of Mr. Maliki’s fragile Iraqi coalition as the triumvirate of leaders from disparate communities on the presidential council attempt to resolve untested parts of the country’s new constitution.

“We insist that the law be implemented and that these men be handed over in accordance with the law,” Mr. Maliki said at a press conference in Baghdad. “The parties concerned were asked to hand over the prisoners, but unfortunately the U.S. Embassy also played a role in preventing their delivery, or trying to hand over some while delaying others.”

At issue is the fate of three top members of the deposed regime, held responsible for the killing of nearly 200,000 Kurds in 1988. They are Saddam’s loyal lieutenant and cousin, “Chemical” Ali Hassan al-Majid, Hussein Rashid Mohammed al-Tikriti, an army commander, and Defense Minister Sultan Hashim Ahmad al-Tai. All were found guilty of war crimes and genocide in June and are currently in coalition military custody not far from Baghdad.

During “Operation Anfal” in 1988, Mr. Majid ordered the deaths of all Kurds living in the north of Iraq. Four thousand villages were razed to the ground; 182,000 Kurds were smothered by mustard gas and the toxic gases sarin, tabun, and VX; and 1.5 million Kurds were deported. Messrs. Tikriti and Hashim carried out the attacks.

There is no doubt about the guilt of the trio, or the brutal nature of their crime. On pronouncing verdict upon them, Chief Judge Mohammed al-Oreibi al-Khalifah of the Iraqi High Tribunal told Mr. Majid: “You gave the orders to the troops to kill Kurdish civilians and put them in severe conditions. … You committed genocide.”

Under the Iraqi constitution, the trio should have been put to death by hanging within 30 days of exhausting their legal appeals, which concluded September 4, but Mr. Maliki postponed their executions because the hangings would have fallen during the Islamic holy month of Ramadan, which ended October 15. Mr. Majid was due to be hanged in the Kurdish town of Halabja.

Iraq’s leading government figures are now divided over how best to proceed. President Talabani, the Kurdish leader, is opposed to the death penalty in principle and is joined by Vice President al-Hashemi, who has said Mr. Hashim was obliged under pain of death to follow Saddam’s orders. Adel Abd al-Mehdi, a Shiite and the third member of the ruling triumvirate, is thought to favor carrying out the sentence without delay.

Mr. Hashim “does not deserve execution, ” Mr. Talabani said in an interview with Al-Arabiya television last month. “He was a capable and excellent officer who implemented Saddam Hussein’s strict orders. He could not disobey orders.”

Mr. Hashemi, the lone Sunni on the council, has threatened to resign if the hangings take place, jeopardizing Iraqi’s frail coalition government.

There is widespread speculation in Baghdad that Mr. Hashim was offered an amnesty by General David Petraeus, now commander of the coalition forces in Iraq, when he gave himself up to allied forces in Mosul in 2003, and that he was in secret negotiations with the Americans to bring about a coup against Saddam ahead of the 2003 allied invasion of Iraq.

While Mr. Maliki insists that the execution should go forward without delay, the presidential council has a different view. Under Iraqi law, the council must sign the execution warrants before the hangings are carried out, but the constitution doesn’t rule on what happens if they fail to agree on the sentence.

Lawyers for the three condemned men, meanwhile, argue that the failure of the council to endorse the sentence amounts to a pardon. The Iraqi courts may be called upon to decide whether the absence of a signature amounts to a pardon or merely a temporary stay of execution.

The American Embassy in Baghdad insists that the fate of the three men is in the hands of the Iraq government and that until the legal dispute is resolved, it will keep the trio in coalition captivity.

The mayhem surrounding the hanging of Saddam in December during an Islamic holiday caused Sunni outrage and international concern at the American handover of the deposed Iraqi dictator, a repetition of which the State Department appears eager to avoid.

“This is an Iraqi judicial process. We think it is very important that the rule of law be respected here and that, when and as necessary, that the time be taken to be sure that all of the issues are clarified,” the American ambassador to Iraq, Ryan Crocker, told reporters in Baghdad.

General Petraeus is proceeding with caution. The coalition forces “are not refusing to relinquish custody” and are waiting for the government of Iraq “to come to consensus as to what their law requires before preparing a physical transfer,” a spokesman for General Petraeus, Colonel Steve Boylan, said in an e-mail to Reuters.