Sinn Féin election candidate John Finucane has reported tweets mocking his solicitor father's murder by loyalist paramilitaries.
The son of Pat Finucane, who witnessed his father being shot dead in the family home in 1989, said one of the tweets expressed regret he was not killed as well.
Pat Finucane, who represented a number of high-profile republicans, was shot by loyalists in front of his wife and three children at their north Belfast home in February 1989.
Mr Finucane, who followed his father into the legal profession, is standing for Sinn Féin in north Belfast.
"I have today made a complaint to the PSNI (Police Service of Northern Ireland) as a result of three tweets that have been sent directly to me," he said.
"These tweets mock and show open support for the murder of my father, who was killed in front of my family and I in 1989.
"One further tweet expresses regret that I too was not murdered along with my father.
"The tweets will now be subject to a criminal investigation along with an investigation by Twitter also.
"Online abuse which enters into criminality cannot and should not be tolerated by anyone in society and I look forward to working with the PSNI in ensuring this is dealt with appropriately," said Mr Finucane.
The killing of Pat Finucane has been shrouded in controversy amid allegations the security forces colluded with the gunmen from the outlawed Ulster Defence Association (UDA).