Iraqi officials tackled piles of ballot papers from a historic referendum on a new constitution after a strong but peaceful turnout that drew many Sunni Arabs back into the political process. Meanwhile, the U.S. and its chief ally Britain have warned Iran over its possible involvement in insurgent bomb attacks in Iraq, top officials said.

Some estimates from Sunni-dominated provinces deemed crucial to the vote suggested they might be split, but members of the Iraqi independent electoral commission in Baghdad urged media to wait until official figures were released.

An initial forecast of the result might be available within two days, with an unofficial tally on Thursday and a final announcement on October 24, though that timeframe could change, senior electoral official Farid Ayyar said.

Over 60 percent of the 15.5 million Iraqi voters were estimated to have cast their ballots, and Saturday was in large part spared the violence that marred elections in January, a peace even more pronounced. In London, U.S. Secretary of State Condoleezza Rice said the constitution had "probably passed," but later adopted a position of wait and see.

"Whatever happens with the referendum, the Iraqi people clearly are taking advantage of the political process to make their views known, and that's bad news for the terrorists," she told FOX television.

Sunni leader Saleh al-Motlag said he estimated most Sunni Arabs, who make up 20 percent of the population, voted "No."

Motlag questioned the validity of any result: "Condoleezza Rice made a statement," he told reporters. "I believe it is a signal to the Electoral Commission to pass the constitution."

"All indications we are getting ... are encouraging and positive for a 'Yes' vote for this constitution. This would be really a major achievement," Foreign Minister Hoshyar Zebari told CNN. "So my guess is, yes, it will be passed."

Carina Perelli, who leads a team of UN advisers working with Iraq officials, stressed that final results were still days away and any early estimates were "impressionistic."

Sunnis turned out in droves to vote, said reporters in Fallujah, Mosul, and Saddam Hussein's hometown of Tikrit.

The charter requires a simple majority for approval but will be rejected if a two-thirds majority in at least three of the country's 18 provinces vote "No."

In the Sunni-dominated province of Salaheddine, which includes Tikrit, election official Saleh Khalil Farraj estimated that turnout was 80 percent, but added that the percentage of 'no' votes was 71 percent.

In Diyala, where Sunnis are also in the majority, the local election commission indicated that 66 percent had voted "yes," amid a turnout that was also 66 percent.

The figures were contested by officials at the commission's headquarters in Baghdad.

Results from the other Sunni-dominated provinces, volatile Al-Anbar, and Nineveh, were eagerly awaited.

Iraqis were congratulated by leaders worldwide. In Washington U.S. President George W. Bush said: "This is a very positive day for the Iraqis, and as well as for world peace."

He added: "I congratulate the Iraqi people, I thank you for meeting this milestone."

British Foreign Secretary Jack Straw said in London: "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."

Russia pledged full assistance to help Iraq in "building and strengthening its new statehood."

Turning her attention to another issue, Rice said Washington had warned Tehran over its involvement in Iraq.

British Premier Tony Blair said this month there was evidence that Iran or its Lebanese Hizbullah allies were the source of sophisticated technology used in roadside bombs, known as improvised explosive devices (IEDs), that have targeted British soldiers in southern Iraq.

"We have tried to deliver a message ... about this issue of IEDs in southern Iraq," Rice said. "We have channels with which to do it. But we use them sternly and pretty specifically to deliver messages."

The Iranian ambassador in London, Sayyed Mohammad Hussein Adeli, told BBC's Radio 4 his country did not support the use of violence against British troops in Iraq and added stability in Iraq was in Iran's best interest.

He said it was not surprising some explosive devices found in Iraq were similar to Iranian devices because weapons from the two countries' eight-year war still litter the region.

Straw, speaking separately to BBC radio, insisted Britain had evidence linking Iran or Hizbullah to insurgent activity in Iraq.

"What we have presented to the Iranians is evidence which in our judgment clearly links the improvised explosive devices which have been used against British and other troops mainly in the south of Iraq to Hizbullah and Iran," he told BBC radio. "We look to the Iranians to desist from anything they have been involved with in the past and to use their very considerable influence with Hizbullah to ensure this continued use ... stops in Iraq."