US Secretary of State Colin Powell said Washington was determined to overcome the "challenges" of Iraq and reaffirmed US support for the interim government after talks in Baghdad.
Powel said that the abductions in Iraq may deter nations from participating in the Iraq rebuilding efforts, but Washington will overcome this problem with courage and determination.
"We are facing challenges in the weeks ahead, but we are determined to overcome (them)," Powell told reporters, flanked by President Ghazi al-Yawar.
Washington's top diplomat is the most senior US official to visit the strife-torn country since the formal winding up of the US-led occupation late last month.
"I reaffirm our determination and commitment to keep working with the interim government as they go about the process of establishing democracy on the basis of freedom and human rights in Iraq," he added.
Powell paid tribute to the Iraqi government, lauding "the courage and determination they have shown in the face of adversity".
For his part, Yawar stressed that Baghdad was dealing with the United States as a sovereign partner and denied that recently appointed US ambassador John Negroponte was manipulating the government.
The largely ceremonial president said the government was "working around the clock" to make sure that elections in January are "held on time".
Just two days after a massive suicide bombing and a wave of attacks across the country left more than 120 people dead, Yawar said the insurgents were "getting more helpless and hopeless".
At least four explosions boomed across central Baghdad during Powell's meetings.
Meanwhile, at least 13 Iraqis were killed and a dozen wounded in overnight clashes between US troops and insurgents in Fallujah hospital sources and police said on Friday.
"We have 13 killed and 13 wounded," said doctor Bilal Jassem at Fallujah's main hospital without indicating if the casualties were civilians or fighters.
The same toll was given by Lieutenant Walid Mohammed of the Iraqi police.
The US military said earlier that it targeted insurgents in Fallujah on Thursday night with artillery and air fire after they attacked a marine position in the city with mortar rounds, rocket-propelled grenades and small arms.
Marines first responded with tanks and artillery fire, it said, adding that there were no marine casualties and "no information about any insurgent losses."
Residents said they heard loud explosions that appeared to come from the Shuhada neighbourhood in the south of the city, targeted by previous US air strikes.
The US military has carried out at least seven air strikes over the past month on suspected hideouts of loyalists of alleged al Qaeda operative Abu Mussab al-Zarqawi, most of them in southern Fallujah.
Mohammed said later that eight people, including five children were admitted to hospital on Friday with wounds when US troops clashed with gunmen near homes in Khaldiya, west of Fallujah, and fired at depot of old military equipment in the city.
There was no immediate confirmation of either incident from the US military.
He said one person was also admitted to hospital after fresh clashes in an industrial zone in South-eastern Fallujah on Friday morning.