The Dubai-based English language daily Gulf News said in an editorial on Monday: "Recent events in Iraq confirm that after three years of occupation by the American-led forces, the issue has become far more problematical and almost insoluble.
"The truth is, the US - or more precisely a stubborn Bush - has got itself into a situation in which it sees no honourable way out.
"Some would argue, therefore, if it cannot be done honourably (thereby justifying the deaths and injuries of all those young American lives) then it must be done anyway, as long as the US gets out.
"There are pundits who claim the inevitable civil war is only being delayed by a US presence, so if it is inevitable, then let the inevitable happen."
Qatari Arabic dailies Al-Watan and Al-Sharq said the "unwise and undue" timing of Saddam's execution could further deepen the factional fracture which all concerned parties were keen to avert.
The papers said it was not easy for the Iraqis to forget the politicised execution of Saddam, screened worldwide, but urged warring rivals "to resort to tolerance and reconciliation to end sectarian violence".
The Lebanese Arabic daily Al-Safir said that Saddam was the first Arab president to be executed under occupation, saying the motivation was political and reflects on the sectarian divide between Sunnis and Shia.
Al Jazeera correspondent Hoda Abd al-Hamid said Baghdad had started to come back to life on Monday, but that traditional New Year's celebrations had not gone ahead.
She said mourning tents had been put up in Tikrit and people were demonstrating near the village where Saddam was buried in a family plot next to his two sons.
Speaking to Al Jazeera, Amal Ibrahim al-Hassan, one of Saddam's sisters, said: "Saddam lived as a hero and died as a martyr. I am proud to be his sister."
One of his nephews, Laith al-Shawi, said: "Saddam did not die. There are millions of Saddams out there."
In New York, the Reverend Jesse Jackson said on Monday that the execution would not make the US safer and would only increase the violence in Iraq.
"Killing him intensifies the violence, reduces our moral authority in the world," said Jackson, who has travelled to the Middle East on peace missions.
"Today we are not more secure. We're less secure. We've missed a moment to appeal to those in Iraq to break the cycle of violence."
The deposed Iraqi president was hanged on Saturday, three years after being captured. He was buried on Sunday.
Jackson, who spoke after preaching at the Canaan Baptist Church in Harlem, said Osama bin Laden, not Saddam, was behind the September 11, 2001, attacks.
"Saddam Hussein didn't hit us. Bin Laden hit us," he said. "Iraq didn't hit us. The Taliban hit us."
Jackson said the US was complicit in the trial and execution of Saddam by the Iraqis "because we held him in our custody, and the government in Iraq today is a government subsidised by the US".