Israeli police announced on Monday an investigation after a photoshopped picture of President Reuven Rivlin wearing a Palestinian scarf emerged amid anger over his decision to reject a soldier's pardon request.

Rivlin had on Sunday refused to pardon Elor Azaria, the soldier convicted of manslaughter for shooting dead a wounded Palestinian assailant as he lay on the ground in March 2016.

Right-wing politicians criticised Rivlin's decision, and Culture Minister Miri Regev went as far as saying that he had "abandoned Elor Azaria and harmed the pardoning institution".

Rivlin's Facebook page quickly filled with messages of support but also scathing criticism, with responders telling him he was "no longer my president," as one wrote, or accusing him of "fawning to appease your Arab and Leftwing friends," as another said.

Populist lawmaker Oren Hazan of the ruling Likud party - the same Rivlin was a member of in Parliament and later as a minister -   called on Rivlin to resign, and said pardoning authority should move from the presidency to the parliament.

The police said they had launched the probe after an image of Rivlin wearing a keffiyah scarf was distributed on social media.

The badly photoshopped picture features a smiling Rivlin on the backdrop of books, with a Palestinian symbol and the words "Reuven Rivlin a traitorous Jew-boy may his name and memory be accursed" in Hebrew.

The statement did not elaborate on those being investigated nor the possible crime committed.