US President George W. Bush said Saddam had received the kind of justice he denied his victims.

Some key US allies expressed discomfort at the execution. And Russia, which opposed the March 20, 2003 invasion to oust the dictator, and the Vatican expressed regret at the hanging which some Muslim leaders said would exacerbate the violence in Iraq.

Bush was asleep at his Texas ranch when the hanging of Saddam was carried out in Baghdad after he had been found guilty of crimes against humanity, the White House said.

He called the execution "an important milestone" on the road to building an Iraqi democracy though he warned in a statement it would not end the deadly violence there.

The US president said Saddam "was executed after receiving a fair trial -- the kind of justice he denied the victims of his brutal regime."

"Fair trials were unimaginable under Saddam Hussein's tyrannical rule," said Bush, calling the trial "a testament to the Iraqi people's resolve to move forward after decades of oppression."

Bush acknowledged that the execution came "at the end of a difficult year for the Iraqi people and for our troops."

"Bringing Saddam Hussein to justice will not end the violence in Iraq, but it is an important milestone on Iraq's course to becoming a democracy that can govern, sustain, and defend itself," he said.

Iran, the influential neighbour of Iraq and arch-foe of the US administration, also welcomed the execution.

"With regards to Saddam's execution, the Iraqi people are the victorious ones, as they were victorious when Saddam fell," said Iran's Deputy Foreign Minister Hamid Reza Asefi, in remarks reported by the IRNA news agency.

Saddam Hussein was reviled in Iran for a 1980 attack that sparked an eight-year war that cost around one million lives on both sides.

Israel, a strong US ally and enemy of Saddam, also hailed the hanging. "Justice has been done," a high-ranking Israeli official told AFP.

"We are talking about a man who sparked fire and bloodshed in the Middle East time and again, and who is responsible for the deaths of thousands of people," said the official on condition of anonymity.

Britain, the main US ally in Iraq, said Saddam Hussein had been "held to account" but reiterated its opposition to the use of the death penalty, as did Australia, another key supporter of the US invasion.

"I welcome the fact that Saddam Hussein has been tried by an Iraqi court for at least some of the appalling crimes he committed against the Iraqi people," said British Foreign Secretary Margaret Beckett.