Two men have been arrested after racist comments about the disappearance of three-year-old Mikaeel Kular were posted on Twitter.
Police said the men, aged 19 and 26, had been arrested, questioned and released on bail.
The tweets were brought to the attention of Police Scotland by members of the public in Edinburgh.
Police Scotland officers liaised with Hampshire and Derbyshire forces to identify the suspects.
On Saturday, Police Scotland said they were investigating another offensive tweet relating to the case which had originated in the Manchester area.
Ch Supt Mark Williams, Police Scotland's divisional commander for Edinburgh, said: "Any reports of racist, offensive or abusive comments made online will be thoroughly investigated and those responsible will be brought to justice.
"If you commit an offence, we will investigate it and you will be prosecuted."
Miss Kular, a mother of five, told police that she put her son to bed at her Edinburgh home at 9pm on Wednesday, but when she went to wake him at 7.15am the following morning he was missing.
She also said that on the night he allegedly disappeared he was sleeping alone in the bedroom he normally shared with his twin sister Ashika.
Officers initially suggested that the little boy may have got up in the middle of the night, put on his clothes, and left the building “for a wander”.
His disappearance led to a large search operation involving hundreds of members of the public who travelled from all over Scotland in a bid to find the youngster, who was described by nursery staff as a “happy wee boy”.
For two days, Police Scotland insisted there was no evidence of criminality, and expressed sympathy for Mikaeel’s “very distraught” mother.