He was the second journalist to be killed in the space of less than two weeks and RSF said it was carried out on the anniversary of previous killings of mediamen.
"The people who murder journalists in Sri Lanka feel so well protected that they carry out fresh murders to mark the anniversaries of their preceding ones," Reporters Without Borders said.
"On the second anniversary of the murder of Tamilnet.com editor Sivaram Dharmeratnam and the first anniversary of the murder of two Uthayan employees, the killers struck again, murdering another journalist with impunity in an area controlled by the army. We call on the authorities to identify and punish those responsible."
RSF said Rajivarnam was shot by a gunman on a motorcycle. Aged 25, he had been a reporter with Uthayan for the past six months.
"He used to go to