* President Macron meets Kurdish Syrian militias
* Kurds say Macron promised more troops as part of coalition
* Turkish advance on Syria's Manbij would be "unacceptable" (Adds details, context, background)
By Marine Pennetier and John Irish
PARIS, March 30 (Reuters) - France could increase its military presence to help a U.S.-led coalition fighting Islamic State in Syria and warned that a Turkish advance on a town controlled by Kurdish-backed militias would be "unacceptable", a presidential source said on Friday.
President Emmanuel Macron has been criticised at home for his response to a Turkish operation against the YPG militia, with opponents saying he has abandoned the Kurds.
The YPG militia makes up a large portion of the Syrian Democratic Forces (SDF), which have been at the forefront of the coalition's strategy to defeat the hard-line militants.
After Macron's meeting on Thursday with an SDF delegation that included the YPG, its political arm the PYD, and Christian and Arab officials, a senior Kurdish official said Macron had promised to send more troops to the area as part of the coalition's efforts, provide humanitarian assistance and "mediate" between the Kurds and Ankara.
That drew a furious response from NATO ally Turkey, which considers the YPG to be an extension of the outlawed Kurdistan Workers Party (PKK), which has waged a decades-long insurgency against the state within Turkey.
Speaking to reporters to clarify the Kurdish comments, a French presidential source said Paris had seen a resurgence of Islamic State in northeast Syria and would continue its fight against the group with the SDF.
"France doesn't foresee any new military operation on the ground in northern Syria outside of the international coalition," the source said.
"(But) if the president felt that, in order to achieve our goals against Islamic State, we needed a moment to bolster our military intervention, then we should do it, but it would be within the existing framework," the source said, without elaborating.
A senior Turkish official had said on Friday a French pledge to help stabilise a region of northern Syria controlled by Kurdish-dominated forces amounted to support for terrorism and could make France a "target of Turkey".
Macron had said in December he expected the campaign against Islamic State in Syria to be completed in February.
Asked about comments by U.S. President Donald Trump that he might disengage from Syria "very soon", the source said Paris had at this stage not received any official request to send reinforcements.
France, like the United States, has already extended arms and training to the YPG-led militia in the fight against Islamic State, and has dozens of special forces based in the region, which has infuriated Turkey.