* NATO faces Trump's demands to do more against militants
* France, Germany open to mission, say it must be limited (Adds more details)
By Robin Emmott
BRUSSELS, Feb 13 (Reuters) - NATO's secretary-general on Tuesday gave his backing for a bigger train-and-advise mission in Iraq after three years of war with Islamic State, heeding a call from U.S. President Donald Trump for the alliance to do more against the militants.
U.S. Secretary of Defense Jim Mattis sent a letter to NATO last month calling for a formal NATO training mission, Reuters reported,, stressing there would be no combat role.
"We have to win the peace," Jens Stoltenberg told a news conference, saying he expected NATO defence ministers to start planning for a bigger mission at a meeting in Brussels on Thursday, with a decision to launch the mission in July.
"It is extremely important to stabilise the country after the combat operations have ended," said Stoltenberg, who visited the U.S. president at the White House last year.
A NATO mission would channel the financial resources of the 29 allies, allow for military commanders to drum up troops and broaden training beyond the capital.
Stoltenberg, who will meet Iraqi Prime Minister Haider al-Abadi at a security conference in Germany later this week, declined to go into troop numbers for Iraq, but said training could include at the defence ministry and on bomb disposal.
NATO currently has a small training team of fewer than 20 people working out of the British embassy in Baghdad that started in early 2017, but is considered by Washington as too small for an alliance of 29 countries with training experience that reaches from the Balkans to Afghanistan.
Stoltenberg's support for a bigger mission is a sign the alliance may be willing to drop its earlier resistance.
European NATO allies fear another open-ended foreign assignment after more than a decade in Afghanistan, but diplomats said France and Germany were showing more openness to a larger Iraq mission, as long as it remains limited in scope.
Turkey will need to be convinced, the diplomats said, noting that a dispute between Ankara and Washington in the fight against Islamic State in Syria had complicated talks on Iraq.
NATO's potential involvement comes as Iraq faces a bill of more than $88 billion to rebuild the country, officials told a donor conference in Kuwait this week. Iraq declared victory over Islamic State in December, having taken back all the territory captured by the militants in 2014 and 2015.
Trump, who as a candidate during the 2016 presidential campaign said NATO would be "obsolete" if it did not do more to combat militants, has urged the allies to act or face more attacks in European cities.
Katie Wheelbarger, principal U.S. deputy assistant secretary of defence for international security affairs, said Mattis was seeking "an enduring NATO presence in Iraq". (Additional reporting by Idrees Ali; Editing by Gareth Jones)
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