The retired US general sent to lead an interim administration has begun assessing the damage the war inflicted on Baghdad, where large parts of the population are still without water or electricity.
Iraq's main Shia groups are boycotting talks with Mr Garner
Jay Garner flew into Baghdad insisting he was a "facilitator not a ruler", but opposition appeared to be growing to the invading forces taking a leading role in the reconstruction.
A Kurdish leader, Jalal Talabani, said he objected to any "foreigner" leading an administration for Iraq.
Groups representing the majority Shia Muslim population have already said they will not co-operate with a US administration and are boycotting talks led by Mr Garner.
Mr Garner and his British deputy Major-General Tim Cross visited a hospital as well as water and power facilities in Baghdad.
Electricity was restored to some parts of the capital a few hours before Mr Garner's arrival, but not to the hospital he went to, which was one of many medical facilities to have been stripped by looters.
Correspondents say the head of the hospital led Mr Garner through dark corridors littered with broken glass and showed him wards bare of everything except beds.
"We will help you, but it is going to take time," Mr Garner told doctors.
He said his aim was simply to get the job done and leave but he refused to comment on a specific timeframe when asked if the work could be completed in three months.
"I wouldn't put 90 days as a mark on the wall. We will be here as long as it takes. We will leave fairly rapidly," he said.
BBC News Online's Martin Asser in Baghdad says there remains some goodwill towards the US-led forces who toppled the regime of Saddam Hussein.
But the role of religious leaders, particularly in the Shia community, will be crucial.
Some have said they will not co-operate with Mr Garner's plans to install an interim administration before Iraqis form their own government and regain control of their country.
Mass protests against the US presence have been mostly peaceful, but residents have told our correspondent that concerns about international troops could soon become more concerted opposition.
Many Shia clerics have already demanded the immediate withdrawal of coalition troops from Iraq.
Kurdish forces allied themselves to the coalition during the war in northern Iraq but Mr Talabani, leader of the Patriotic Union of Kurdistan, told Dubai's al-Arabiyah television that he too believed the US had no political role in Iraq.
"We do not accept a foreigner heading an Iraqi government," he said.
"This government has to be a coalition, an interim one, and an Iraqi one.
"It would also be in charge of paving the way for holding democratic elections in order to form a founding council that would draft a formula for future Iraqi rule.
Only Ahmed Chalabi, leader of a political grouping backed by some elements within the US Government, has called for US troops to remain in Iraq for up to two years until elections can be held.
The leader of the Iraqi National Congress (INC) also insisted that there was no religious figure waiting to take power in Iraq.
His comments came as tens of thousands of Shia Muslims continued their march to the holy city of Karbala on a pilgrimage that had been banned under Saddam Hussein's government.
In other developments:
- The US military says it has captured Saddam Hussein's former minister of higher education and scientific research, Abd al-Khaliq Abd al-Gafar, while the INC reports that Saddam Hussein's son-in-law, Jamal Mustafa Sultan, has given himself up
- The US is reported to be planning a long-term defence relationship with Iraq's future government, which could allow US forces to be reduced in other parts of the Gulf region
- US President George W Bush says he sees "positive signs" that Syria is heeding the US call not to shelter fugitive Iraqi officials
- Iraqi oil officials reportedly begin talks on resuming production, which was suspended nearly a month ago at the outbreak of war
- The US has refused to recognise Mohamed Mohsen al-Zubaidi as the new governor of Baghdad. Mr Zubaidi claims he was elected by a broad-based grouping.