* Hollande says other crises should not distract from Syria
* French FM calls perspective of Assad re-election "grotesque"
By John Irish
PARIS, March 15 (Reuters) - France will not "close its eyes" to the Syrian conflict despite other crises taking centre stage, French President Francois Hollande said on Saturday, promising to increase efforts to reach a political solution.
More than 140,000 people have been killed and 2.5 million have fled abroad as refugees in an increasingly sectarian civil war. The conflict began with mass street protests against Syrian President Bashar al-Assad in March 2011 but turned into an armed insurgency after he cracked down violently on demonstrators.
"This is a tragedy that has lasted three years ... there are massacres taking place every day, a (peace) conference was held in Geneva that didn't succeed, but we must continue to apply crucial pressure so that a political solution can be found," Hollande said alongside Italian Prime Minister Matteo Renzi.
France, one of Assad's fiercest critics, was the first Western power to provide non-lethal military aid to rebels. It was also the first Western state to recognise the opposition National Coalition as the sole representative of the Syrian people.
"Certain subjects disappear from the news, not because nothing is happening - often the worst things are happening - but because other news takes its place," Hollande said referring to the crisis in Ukraine.
"I think that, as long as there are these massacres, this tragedy, these refugees, displacements and women getting raped for the rights they defend, then we have not finished with Syria," he said.
"France, just like Italy, does not intend to close its eyes."
The Syrian government has been making incremental gains in recent months, regaining the initiative in the conflict. Emboldened by the failed peace talks in Geneva and with ongoing support from Iran and Russia, Assad is looking increasingly likely to stand for a third term in July.
If he does so, in defiance of the opposition and Western leaders who have demanded he step down, that would end the U.N.-backed Geneva peace process, which was predicated on steps towards a democratic transition.
Syria's parliament set residency rules for presidential candidates, state media said on Friday, a move that would bar many of Assad's foes who live in exile.
"Everything must be done so that a free, democratic Syria emerges that respects the diversity of Syrian society," French Foreign Minister Laurent Fabius said in a statement to mark the third anniversary of the conflict.
"This (Geneva) mandate fixed by the United Nations makes the perspective of a grotesque re-election of Bashar al-Assaad null and void," he said.