Police are seeking voluntary interviews with those who attended the funeral of veteran republican Bobby Storey in Belfast in June.
Detectives are investigating potential breaches of Northern Ireland’s coronavirus regulations on gatherings.
Mourners on June 30 included senior Sinn Féin representatives like Deputy First Minister Michelle O’Neill and Finance Minister Conor Murphy.
Deputy Chief Constable Mark Webster of Cumbria Constabulary was appointed to oversee and direct the Police Service of Northern Ireland (PSNI) inquiry.
He said: “Today an initial number of letters were issued to individuals who were identified as having been present on 30th June in potential breach of the health protection regulations.
“The letters are inviting these individuals to participate in a voluntary interview with investigating officers at a local police station.
“Upon receipt of a letter, individuals will have 14 days to respond should they wish to take part in an interview.”
Ms O’Neill and Mr Murphy have denied breaching social distancing measures while at the funeral.
Hundreds of people lined the streets in west Belfast as Mr Storey’s funeral cortege passed by despite the restrictions and despite marshals being present.
A row with the DUP over the matter prompted the suspension of joint briefings with Sinn Féin during the health emergency.