Mr. Brahimi says America should tread carefully in Fallujah. He says an all-out assault on insurgents who refuse to disarm would ultimately do more harm than good.

"If you have enemies there, this is exactly what they want you to do - to alienate more people so that more people support them," said Mr. Brahimi.

During an interview recorded Friday for the ABC television program This Week, Mr. Brahami stressed that as a diplomat, he always supports alternatives to military action. He said that is the case in Fallujah, the hotbed of Iraqi resistance west of Baghdad, and in Najaf, a holy city for Iraq's Shiite majority.

He noted Najaf, where a cleric is urging followers to resist coalition forces, also has historic significance.

"Sending the tanks rolling into a place like this is not the right thing to do, and I think the Americans know that extremely well now," he said.

Mr. Brahimi has won support from the White House for his plan for an interim Iraqi government that will stay in power until elections are held. One person not believed to be on his list of possible members is Ahmed Chalabi, who sits on the current governing council.

On the Fox News Sunday program, Mr. Chalabi said Lakhdar Brahimi is an Algerian with an Arab nationalist agenda, who is not a unifying figure in Iraq. He took issue with the notion of restraint in Fallujah and urged the coalition to take decisive action.

"Those terrorists and Baathists are holding the people of Fallujah hostage," he said. "We must release the hostages."

Also appearing on the Sunday-morning news programs in the United States was the Saudi Ambassador to Washington, Prince Badar bin Sultan. When asked whether coalition forces should invade Fallujah, he said that is a decision that is in the hands of President Bush. But the ambassador stressed he personally believes a negotiated solution would be best.

Prince Bandar was also queried about his discussions with the Bush White House about the war, the region and the price of oil. On NBC's Meet the Press, he denied once again that Saudi Arabia pledged to drop oil prices right before the U.S. presidential election in November.

But he did not dispute that he suggested prior to the war that the Iraqi army should not be disbanded, and its members should be given several months pay by the United States.

"I do not talk about my conversations with the president," said Prince Bandar. "But I believe that would have been the right way to go."