"I think it would be helpful to have a conference that brings everybody together, along the lines of what we did in the former Yugoslavia and others," Annan said.
But Al-Hakim called the proposed conference "illegal" and "unrealistic".
Al-Hakim, whose US visit comes hot on the heels of a Thursday meeting between Bush and Nuri al-Maliki, the Iraqi prime minister, said Iraqi democracy did not need such outside help.
"We have a political process and our government is one of the strongest in the region"
Abdel Aziz al-Hakim, the Iraqi Shia leader
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"We have a political process and our government is one of the strongest in the region thanks to its popular base of 12 million voters," said Hakim, whose SCIRI is key to Iraq's ruling Shia alliance.
"This government was formed on the basis of a coalition and it is therefore unacceptable for the Iraqi people that these questions should be debated at international conferences."
Al-Hakim said the Bush meeting had been "prepared a long time ago".
"We will discuss developments of the situation in Iraq in order to look at it all together - the US has a major presence in Iraq and an influence on events."
"There are numerous questions that need to be discussed and clarified, which need to be decided on," he said, without elaborating.
Al-Hakim has warned that the outbreak of a civil war in Iraq pitting Sunnis against Shia would spell disaster for the violence-plagued country and the entire region.
Sergei Ivanov, the Russian defence minister, added his voice to Annan's when he said his country too will would seek the convening of an international conference involving neighbouring countries to discuss the Iraqi crisis.
Interviewed by Aljazeera, Ivanov described a proposed division of Iraq as a "horrible scenario".
In other news, Stephen Hadley, the US national security adviser, said the US administration will announce at the right time changes to its Iraq policy after discussing the matter with Iraqi leaders.