Story Highlights• Witness: There was "dancing around the body"
• Power outage delayed spread of the news to Iraqi citizens
• Baath Party had warned death would trigger "grave consequences"
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(CNN) -- A witness to Saddam Hussein's execution in Baghdad said that celebrations broke out after the former dictator died, and that there was "dancing around the body."
"Saddam's body is in front me," said an official in the prime minister's office when CNN telephoned. "It's over."
In the background, Shiite chanting could be heard. When asked about the chanting, the official said "These are employees of the prime minister's office and government chanting in celebration."
Video showed Iraqis celebrating in the streets of Najaf, a Shiite holy city. (What jubilant Iraqis chant, bang drums )
The execution took place shortly after 6 a.m. (10 p.m. Friday ET), Iraq's national security adviser, Mowaffak al-Rubaie, told Iraqi television.
A power outage delayed the spread of the news to Iraqi citizens. But as word got out, gunfire broke out in the capital's streets. It was unclear whether the shooting was celebratory in nature.
Temperatures hovered around freezing hours after the hanging at the start of a Muslim holiday, and CNN correspondents reported relatively few Iraqis on the streets of Baghdad.
Feisal Istrabadi, Iraq's U.N. ambassador, told CNN the execution was "a very solemn moment for me."
"I can understand why some of my compatriots may be cheering. I have friends whose particular people I can think of who have lost 10, 15, 20 members of their family, more," Istrabadi said.
"But for me, it's a moment really of remembrance of the victims of Saddam Hussein."
Prime Minister Nuri al-Maliki did not attend the execution, according to an adviser to the prime minister interviewed on state television. Al-Maliki is a member of Iraq's Shiite majority, which was oppressed during Hussein's reign.
"Let us turn over this dark page of Iraqi history and let us look forward to building Iraq together," al-Maliki said after the execution.
The nation has been plagued by violence since the U.S.-led invasion toppled Hussein in 2003, and sectarian bloodshed escalated this year after the February bombing of a Shiite shrine in Samarra.
The Baath Party, the political movement that ruled Iraq during the Hussein era, warned this week that there would be "grave consequences" if Hussein were executed.
Saying it would hold the United States responsible, a message appeared on albasrah.net Tuesday that read: "The Baath and the resistance are determined to retaliate in all ways and all places that hurt America and its interests if it commits this crime."
The largely Sunni-Arab Baathists said they also would retaliate against members of the Iraqi High Tribunal. (Baath warning)
'End of an era'
Rubaie said the execution was videotaped and photographed extensively from the time Hussein was transferred from U.S. to Iraqi custody until he was dead. State television reported that those images will be distributed to the media.
"This dark page has been turned over," Rubaie said. "Saddam is gone. Today Iraq is an Iraq for all the Iraqis, and all the Iraqis are looking forward. ... The [Hussein] era has gone forever."
"He was a broken man," he said. "He was afraid. You could see fear in his face."
Vali Nasr of the U.S.-based Council on Foreign Relations told CNN that Hussein's death marked "the end of an era."
Nasr and another Iraq expert, John Alterman of the U.S.-based Center for Strategic and International Studies, said the big question now is: "How do you put Iraq back together?"
Nasr said Hussein's death threatens to deepen the divide between Shiites and Sunnis because Hussein represents the last time the minority Sunnis held power in Iraq.
Nasr cited speculation that some Kurds are disappointed Hussein would not stand trial for crimes against them.
In Crawford, Texas, President Bush welcomed the news of the execution.
"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. (More world reaction)
CNN's Arwa Damon, Elaine Quijano and Aneesh Raman contributed to this report.