A meeting of ambassadors at the alliance's headquarters in Brussels to resolve stark differences in views failed to reach a compromise.
A NATO official said the envoys would meet again later in the day, though it was not immediately clear whether France would ultimately block the others' determination to launch the training mission inside Iraq as early as next month.
"There will be another meeting today ... because more discussion is needed," a NATO official said, declining to give details of the closed-door talks.
The meeting was expected to convene at about 6pm (1600 GMT).
NATO leaders meeting in Istanbul last month promised support to the interim Iraqi government, which asked the alliance for military equipment and protection for UN personnel as well as training for both its troops and border guards.
France wants more clarity on the
nature of required aid to Iraq
But the wording of the summit accord was deliberately vague because of French and German resistance to an overt or collective role for the alliance inside Iraq - which is why the envoys are now back around the table hammering out the details.
France was Europe's fiercest opponent of the US-led war on Iraq. Critics accuse it of seeking to undermine NATO by trying to curb US influence.
Diplomats said Paris is determined not to hand US President George W Bush a show of international support for his Iraq policy before the Republican Party's pre-election convention, which opens at the end of August.
Germany and Belgium are not enthusiastic about a NATO training mission in Iraq but have made it clear that they would not stand in the way of the majority.
"France's position has not changed," a Foreign Ministry spokeswoman in Paris said. She referred to comments made in Istanbul by French President Jacques Chirac, who said NATO could offer support to individual nations which wanted to train Iraqi troops but "a NATO presence in Iraq" was out of the question.
"It looks like France is blocking an alliance consensus," said one diplomat at the 26-nation alliance's headquarters as the ambassadors went into their morning talks.
"There are 20-plus countries in favour of beginning the training mission inside Iraq next week, two or three are undecided - and there's one country blocking, that's France."
Who will pay?
Paris wants more clarity on what security would be provided for trainers - even though, like Germany, it has vowed not to deploy any of its own nationals - how much training would be inside Iraq and how much abroad, and who will pay the costs.
It is also opposed to putting a NATO mission under the operational command of the US-led forces in Iraq.
A team of NATO experts recently went to Iraq to explore options. France, which says there are still too many unanswered questions, has argued for the despatch of a second fact-finding mission which would report back to the alliance in September.
"There are 20-plus countries in favour of beginning the training mission inside Iraq next week, two or three are undecided - and there's one country blocking, that's France"
Nato diplomat in Brussels
The standoff on training echoed a blazing row at NATO before the Iraq war last year, when France, Germany, Belgium and Luxembourg blocked a consensus on sending military reinforcements to Turkey, one of Iraq's neighbours.
Paris was the only one to hang tough in that dispute, and in the end allies resorted to the Defence Planning Committee - on which France has no seat because it is not part of NATO's integrated military structure - to authorise the plan.