His statement on Thursday said the government - chosen by the UN, the US-appointed Iraqi Governing Council and US officials - lacked "electoral legitimacy" but remained a step in the right direction and would succeed if specific goals were met. It had "mammoth tasks" ahead, said al-Sistani.
"The hope is that this government will prove its worthiness and integrity and its firm readiness to perform the mammoth tasks it is burdened with."
In a hand-written statement, the Iranian-born cleric listed security, basic services, the organising of elections and a new UN resolution as key goals.
Al-Sistani's objections to US policy in Iraq effectively derailed at least two blueprints put forward by Washington to chart the political future of Iraq.
Another leading Ayat Allah, Muhammad Said al-Hakim, also gave tacit support to the new interim government, but insisted the UN had a responsibility to bring "full sovereignty" to Iraq as soon as possible.
The elderly cleric had demanded elections to choose the government to take power from the US-run occupation at the end of this month. But he dropped his insistence after UN envoy al-Akhdhar al-Ibrahimi decided that an early ballot was not possible due to the security situation in this country.
Iraqis will choose a transitional government by the end of January and then elect a new administration after ratification of the new constitution next year.
With the new government set to take over in weeks, al-Sistani said the main tasks were to secure Iraq's sovereignty, relieve the suffering of the people, restore security and prepare for the January elections.
Their statements came as fighting raged on in the occupied country. Five Iraqi civilians were killed and 15 more wounded when fighting erupted between US troops and a Shia Muslim militia in Kufa.
Speaking from the Furat al-Awsat hospital on Thursday, Dr Muhammad Khazim said children were among the casualties in skirmishes that began around 04:00 local time and lasted four hours.
A grouping of mainstream politicians and other dignitaries blamed US troops for the collapse of the latest truce in the area announced on Tuesday by the US-appointed provincial governor, Adnan al-Zurfi.
The Shia militias in Kufa and Najaf
have suffered terrible losses
On Wednesday, nine Iraqis were killed and 44 wounded in ferocious clashes in the same city and in Najaf, as well as the Baghdad suburb of Sadr City where the Shia cleric Muqtada al-Sadr enjoys significant support.
Shia resistance to occupation has increased since early April after US troops announced a series of measures against the young cleric, including the closure of one of his newspapers and the arrest of a key aide.
In Diyala province, northeast of Baghdad, an Iraqi security officer was killed when an unidentified armed man opened fire in the market, reported Aljazeera's correspondent.
In Baquba, some 60km north of Baghdad, three Georgian occupation soldiers were lightly wounded in a resistance attack, said the foreign ministry in Tbilisi.
In the northern city of Mosul, a US patrol came under attack but there were no casualties among the occupation, said Aljazeera.
US forces detained three cameramen working for foreign agencies apparently under investigation.
Further north in the city of Kirkuk, a huge explosion rocked a US military base. The cause of the blast and whether there are any casualties is unclear.
In a separate incident, explosions rocked a major US military base outside the oil-rich city of Kirkuk.
Shrouding the city in smoke, district police chief Burhan Tayyib Tahib confirmed a Katyusha rocket hit an arms store.
Tahib said he knew of no casualties among civilians outside the base, which covers a wide area. A US military spokesman said there had been an "incident", but had no further details.
Shells and rockets screamed into the night sky over the base near the main airport of the oil-rich region. The initial blast was followed by sirens on the base and mayhem that was still going on nearly two hours later.
"You can see rockets flying and landing all over the base," reporter Adnan Hadi said from a vantage point 500m from the base's perimeter.
"The windows of buildings close to the base have all been shattered," he said.