The Iraqi government has welcomed a positive report on the progress of the US military surge in Iraq by the top US commander there.
Iraqi National Security Adviser Mowaffaq al-Rubaie praised the US' "enormous sacrifice" and predicted a reduced combat role for US troops.
Gen David Petraeus told a Congressional panel violence had declined since more US troops were sent to Iraq.
But his verdict was heavily criticised by US opposition politicians.
Gen Petraeus said "security incidents", including sectarian violence, had declined since the start of the surge.
In his testimony before a joint hearing by the House of Representatives Armed Services and Foreign Affairs committees, he said he thought around 30,000 troops could be withdrawn by the middle of next year.
US ambassador to Iraq Ryan Crocker has also been testifying.
Iraq's Mr Rubaie said Iraq was prepared for the US to reduce its forces.
"We anticipate in the near term a relaxation of the requirement for coalition forces to be in direct combat operation," he told a press conference in Baghdad.
But he warned against a quick withdrawal of US troops, saying: "We know that for some time we will continue to need the support of coalition forces."
The BBC's Andrew North in Baghdad says residents of the Iraqi capital agree that violence has fallen - but not enough to allow them to leave their homes without fear.
Meanwhile, an opinion poll suggested about 70% of Iraqis believe security has deteriorated in the area covered by the US military "surge" of the past six months.
The survey for the BBC, ABC News and NHK of more than 2,000 people across Iraq also suggested that nearly 60% see attacks on US-led forces as justified.
Gen Petraeus and Mr Crocker were due to face further questioning in Congress on Tuesday.
The BBC's Jonathan Beale in Washington says US President George W Bush hopes the two men's sober but overall positive assessment will now make it much harder to argue for America to pull out of Iraq.
But their presentation is unlikely to significantly alter US public opinion or even shed any new light on the war, our correspondent says.
Indeed they were heavily criticised by some politicians for their upbeat assessment on Monday.
House Foreign Affairs Committee Chairman Tom Lantos said the surge was a strategic failure, and that it was time for troops to leave.
"We need to get out of Iraq, for that country's sake and for our own. It is time to go," he said.
Another Democrat Congresswoman, Lynn Woolsey, told the BBC Gen Petraeus was a "mouthpiece" of the White House, a position that he has flatly denied.
But Republican Duncan Hunter defended the general, saying US progress had led to gains by Iraqi security forces, including an army which was "beginning to emerge as a professional force".
A record 168,000 US troops are now in Iraq after 30,000 arrived in the surge between February and June.