The new government of Iraq faces daunting obstacles in restoring security and tranquility, but Prime Minister Iyad Allawi (search) is "a tough guy" and can do the job, the former U.S. administrator said Wednesday.

Standing on the North Lawn of the White House for appearances on several morning network news shows, L. Paul Bremer III (search) voiced confidence that the new Iraqi government will surmount violence and stabilize conditions on the ground.

"The most important priority of this new government is, of course, security," he said on CBS's "The Early Show."

"They must get security down to the level where violence allows them to go forth with elections in January," Bremer said. "The prime minister is a tough guy ... the survivor of a brutal assassination attempt" several years ago.

Bush called Bremer to the White House for lunch Wednesday, two days after the diplomat left Iraq, to thank him for his efforts.

"American certainly owes Ambassador Bremer a debt of gratitude for his work over the last 14 months," said White House spokesman Scott McClellan.

Ultimately, Bremer said, he expects that Iraq "will certainly be a pluralistic society. It will not be an American-style democracy. It will be Iraqi style. I think it will be a successful country and I think it will be quite an example for other countries in the region."

Bremer told ABC's "Good Morning America" he believes the Iraqi security forces being trained to take over securing the country can succeed but that a difficult month is ahead.

"I'm confident that as we get the leadership training in place with the security forces, they will be able to defend their country and they will get the security situation — not totally calm, but under control," he said.

Bremer said he thought it would be months before former Iraqi dictator Saddam Hussein (search) or others would be brought to trial before an Iraqi tribunal, but said he was confident the Iraqis would handle it well.

"He will get the kind of justice he denied his own people," Bremer said. "It's a wonderful day for the Iraqis to get him under their direct control. It will be a major event."

But he also said the Iraqi leaders must be vigilant in their handling Saddam. He said transferring physical custody of Saddam to the Iraqis inevitably will occur soon but that he did not know how soon.

Bremer said on NBC's "Today" show there could be a scenario in which Iraqis impatient with a drawn-out legal process might try to take Saddam and "hack him to pieces" before he can be brought to trial.

"That's a likely scenario," he said.

Asked if security concerns had forced the United States to choose a very low-key setting for handing sovereignty back to the Iraqis, Bremer said he had always anticipated "a modest and dignified ceremony." The only change was moving the date from Wednesday to Monday, he said.

Asked on CBS if he was surprised at the lack of violence surrounding the return of sovereignty, Bremer replied, "No. One of the things that we have always hoped is that once the Iraqis had full responsibility for their country, a lot of people who were doing these attacks against the provisional coalition ... would be attacking the Iraqi people."

"What is good now is they (the new Iraqi governmental leaders) are responsible. It's their country. It's a very good government, a government that is enjoying high support," he said, "and this government is now in the hands of Iraqis."

Asked in retrospect if it was a mistake to disband the Iraqi army after Saddam was toppled, Bremer demurred.

"I didn't actually disband it," he said. "There was no Army to disband. They all went home. This is one of those great myths. ... I would have had to recall an Army."

Such a move, Bremer said, "could very well have set up major violence."