"I think the important achievement of yesterday, which was a great day for Iraq, was that the Sunnis, who had not participated in the political process, did participate this time," Zalmay Khalilzad said on ABC television on Sunday.
"I think we are making good progress. Yesterday was a good indication that our approach to the Sunnis is producing results.
"This is the first time, yesterday, that they have participated in significant numbers," said Khalilzad, who had a key behind-the-scenes role in bringing about the draft and the referendum.
More than 61% of registered Iraqi voters took part in Saturday's referendum on a permanent constitution, which, if approved, will open the way for general elections in December for a new government.
Participation by Sunnis was in doubt due to their belief that key elements of the document would fragment the country into disparate ethnic sections.
"With the continuous Sunni participation in the political process, and with Iraqi and coalition security forces isolating and defeating the insurgent, that's the recipe ... for success"
US Ambassador to Iraq
Nevertheless, voting occurred against a backdrop of relative calm, with violence that has engulfed Iraq for months dipping.
Khalilzad attributed the lull to successful security measures by Iraqi and US-led forces.
"Yesterday was indeed a good day," he said.
"What it also indicates is that violence is not the way to deal with problems, that violence is a dead-end street.
"With the continuous Sunni participation in the political process, and with Iraqi and coalition security forces isolating and defeating the insurgent, that is the recipe ... for success," the ambassador said.
Arab League Secretary-General Amr Moussa said on Sunday that Iraq's vote on a draft constitution was a step in the right direction, while noting the need for national reconciliation.
Moussa told a Cairo press conference that he hoped the results would soon be announced, but "in parallel, one must work towards national reconciliation, a general understanding of the country's future and the preservation of its territorial unity and stability and relations between its various communities."
An Arab League official said earlier that Moussa would travel to Iraq on Monday for talks aimed at preparing a "national dialogue" under the auspices of the pan-Arab organisation.
Amr Moussa is planning to travel
to Iraq on Monday for talks
Moussa refused to confirm the date of his visit.
A league delegation sent to Iraq to prepare for the visit was ambushed last Monday. Two Iraqi commandos guarding the convoy were killed and seven wounded.
Meanwhile, British Foreign Secretary Jack Straw on Sunday hailed the weekend referendum as a major step on the path to creating a democratic and peaceful Iraq.
In a televised statement, Straw also called Saturday's vote "very good news for all Iraqis" and noted that "the whole process took place in remarkable calm given the overall security situation" in the country.
"What this referendum shows is the hunger of Iraqis to exercise the same rights that the rest of us have, democratic rights, and to defy the terrorists.
Straw thinks the referendum
will create a peaceful Iraq
"Whatever the result, it is a major step on the way to establishing a democratic, and we hope, peaceful Iraq," Straw added.
An initial results forecast might be available within two days, with an unofficial tally on Thursday and a final announcement on 24 October, though that timeframe could change, senior electoral official Farid Ayyar said.