But he said: "Our intention is not to send French soldiers to Iraq."
A US official said on Friday that Condoleezza Rice, the US secretary of state, had thanked Kouchner for his visit to Iraq.
The unnamed official was reported by the AFP news agency as saying Rice spoke to Kouchner by telephone on Thursday and "thanked him for his visit".
On the ground in Iraq, violence continued unabated.
In Baghdad, US forces in the primarily Shia neighbourhood of Shula clashed with fighters on Friday.
The skirmish broke out when a pre-dawn US military patrol came under small arms and machine-gun fire from rooftops and called in helicopter support, Lieutenant-Colonel Scott Bleichwehl, a US army spokesman, said.
"Had the US foreign policy makers read history, they would not get involved in any war after Vietnam"
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Reports differed as to the number of people killed in the fighting.
Dr Mohammed Abbas, from the Al-Noor Hospital in Shula, said the facility had received 13 corpses.
"Those dead were killed by shrapnel and two of them are women," he said, suggesting that some of the dead could be civilians.
"We have also admitted 15 wounded people."
But Nassar al-Rubaie, head of a 30-member bloc in parliament loyal to Muqtada al-Sadr, the Shia leader of al-Mahdi army militia, said that 21 civilians had been killed, a "large number" wounded and several houses destroyed in the Shula fighting.
Al-Sadr's main office in Baghdad reported 14 civilians killed and 20 others injured.
Hundreds of Iraqi Shias later took the dead to the central holy city of Najaf for burial, loading the coffins, draped in Iraqi flags on taxis and vans.
Earlier in the week, Iraqi troops and US Special Forces raided a home in the Hiyt area and seized an suspected an al-Qaeda fighter suspected to have shot down a US helicopter in 2004, the US command said on Friday.
The forces detained the suspect and a "second person of interest" in the raid on Wednesday, and found an assault rifle as well as numerous identification cards and passports.
In addition to the helicopter attack, the primary suspect, whose name has not been released, is said to be involved in roadside bombings and sniper attacks on US and Iraqi forces in the region, a military statement said.
US forces also reported killing seven fighters and detaining 12 others in operations aimed at disrupting al-Qaeda in central and northern Iraq.
On Thursday, masked fighters drove into the city of Samarra, 125km north of Baghdad, at dusk in about 20 vehicles, then split into small groups and assaulted four police checkpoints and a headquarters building, according to a police official.
One policeman and two civilians, a woman and an 11-year-old girl, were killed in the fighting and nine people were injured, including a police commando and three children, he said.
Lieutenant-Colonel Michael Donnelly, a US military spokesman in northern Iraq, said he had no details on the Iraqi incident.
He acknowledged that an American patrol had been in a clash with fighters in the city on Friday.
The US command said one soldier was killed on Friday in an explosion in Salahuddin province, which includes Samarra, and four soldiers were wounded.
It was unclear whether the incident in Samarra was the same one reported by Donnelly.
Two of the fighters were killed and another captured, Donnelly said.
There were no immediate reports of US casualties.