The North Atlantic Treaty Organisation (NATO) agreed in principle at a summit in Istanbul last month to provide such training after the handover of powers to Baghdad from the US-led occupying forces.
But they left details to be hammered out, with Paris and some other countries battling with Washington to determine exactly how the mission will be implemented, officials said.
One NATO official was upbeat after a first meeting of ambassadors on Thursday morning. "They are narrowing down the outstanding issues," he said.
But later in the day, as NATO ambassadors resumed for an evening session of talks, French officials were less upbeat saying that there was still a "fundamental problem".
France had previously resisted NATO having a permanent flag in Iraq. But the key problem now seems to focus on who exactly will command the mission.
"We have reached a real problem: to what degree the training mission will be merged or not into the multinational force down the road," said a French official, adding that other countries backed the Paris stance.
"We have to restore our respect in the world to bring our allies to us and with us."
John Edwards, US Senator
"For France and five or six other countries this is a problem," he said.
He added that France would be willing for a preliminary NATO training team of some 20-30 officers to travel to Iraq in August to conduct initial high-level training, and then to report back to NATO leaders in September.
But the US, which is seeking a "double-hitting" command structure for the training mission, wants decisions now for how the mission will pan out after the summer as well.
The US, which has long pushed for a bigger NATO role in Iraq where American troops have been struggling to contain mounting violence, is pushing hard for an accord.
A NATO military delegation led by US admiral Gregory Johnson was dispatched to Iraq at the start of July to study options for the mission.
Diplomats said a second military mission could be sent to Iraq to clarify options.
NATO Secretary-General Jaap de Hoop Scheffer said on Monday that he hoped for an agreement by the end of this week on a training mission, both inside and outside Iraq.
Earlier this month Iraq's interim Foreign Minister Hushiar Zibari, part of the Iraqi administration which took over in June, urged NATO to make good quickly on its promise to train security forces.
Zibari said authorities were "in a race against the clock" in their effort to ensure stability.
Differences over leadership have
placed the US and France at odds
Armed resistance and crime has soared in Iraq following the US-led invasion with hundred of thousands Iraqis unemployed. Meanwhile politically motivated seizing of foreign nationals working with US-led occupation forces and authorities soar.
Another NATO official denied earlier Wednesday that the differences were in any way comparable to the splits which shook NATO to its foundations in the run-up to last year's US-led war against Iraq.
On that occasion France, Germany and Belgium effectively paralysed the alliance - which requires unanimity for all decisions - by refusing to allow NATO to come to Turkey's aid.
"NATO is very keen to finalise this package ... but don't look for repetitions. History does not repeat itself," the official said.
Democrats and NATO
US Senator John Edwards said on Wednesday that if he and Democratic presidential candidate John Kerry win the White House in November, they will restore America's respect in the world and persuade NATO to play a greater role in Iraq.
"We have to restore our respect in the world to bring our allies to us and with us," Edwards said. "It's how we won the world wars and the Cold War, and it is how we will build a stable Iraq."
Edwards addressed the Democratic National Convention in Boston immediately before the delegates were to formally nominate Kerry to head their ticket in November's election.