Election posters are being replace by posters promising an end of to occupation
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Iraq's electoral commission says 1.6m ballots have been counted at its headquarters over the past two days.
The ballots represent about 10% of registered voters, poll officials said.
Partial results show the United Alliance, backed by Shia cleric Grand Ayatollah Ali Sistani, leading with more than one-million votes.
The Alliance's nearest rival so far is the list of candidates led by interim Prime Minister Ayad Allawi, with about 360,000 votes.
The partial results come from six of Iraq's 18 provinces - Baghdad, Dhi Qar, Muthanna, Qadisiya, Najaf and Karbala.
Officials also said they had sent a team to the northern city of Mosul to look into allegations of irregularities in Sunday's election.
There is no indication about when the final results will be known, but they will not be published until they are double-checked, the officials said.
Election officials warned that it might take another six days before certified results are announced, and even that timeframe may slip.
Irregularities
Threats of violence did not deter large numbers of electors voting on 30 January, but there were complaints about polling stations running short ballot papers in several provinces.
A team of three lawyers is being sent to ethnically-mixed Mosul - Iraq's third biggest city - to investigate alleged irregularities.
The UN wants Sunni Muslims to take part in the next stage
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"We received some complaints and the legal department in our commission is studying these complaints thoroughly," said election commission official Safwat Rashid.
Sunni Arabs in particularly complained about being denied the right to vote around Mosul.
The United Nations chief envoy in Iraq, Ashraf Qazi, has held talks with the leader of the main Sunni Muslim political party, the Iraqi Islamic Party (IIP).
On Wednesday, the main Sunni religious organisation, the Associations of Muslim Scholars, said the election had been illegitimate as so many Sunnis Muslims had not taken part in the vote.
Mr Qazi expressed the hope that all sectors of Iraqi society would "participate in drawing up the constitution... and our efforts will continue in this direction".
IIP leader Muhsin Abdul Hamid said talks had centred on "the next government, the constitution and how to bring about co-operation to sort out Iraq's affairs".