"They continue to do broad-scoped operations across all of Iraq. We continue to help them as they do these, and that will continue after 1 September," when the US contingent will have dropped to 50,000 soldiers and US combat operations will have ceased.
"But we do believe they are ready to assume full operations in Iraq," he added.
Odierno stressed that he thought Iraqis were making progress towards putting together a new government, even as some US and Iraqi officials fear swelling violence in the country if political negotiations, undertaken since the March 7 elections, fail.
"I think we'll see some first steps toward forming a government by 1 September," he said, as he appeared to encourage resolution to the political crisis sooner rather than later in order to avoid continued perceptions of weakness that could be exploited by extremist groups.
"It's important for the Iraqis to understand the importance of moving forward quickly, and I think we're starting to see that as we see negotiations pick up over the last couple of weeks," he said.
Weekend violence left at least 60 people dead across Iraq, including 43 killed in a trio of bomb blasts late Saturday in the southern city of Basra.
The US deployment in Iraq reached its peak in 2007 at 170,000 troops but their presence has gradually diminished over the past 18 months.
Some 70,000 soldiers are currently on the ground in the country, and Washington plans to reduce that quota to 50,000 -- all in non-combat brigades -- by August 31.
US President Barack Obama has promised a complete withdrawal by 2011.
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