“Our investigation is ongoing and we are working tirelessly to determine the exact circumstances of this tragedy,” he said.
Det Ch Insp McGuinness also asked the public if they had any information that may be of use to the Police Service of Northern Ireland (PSNI) to come forward.
The shooting happened in a rural area about 75 miles (121km) west of Belfast and about eight miles from the county’s largest town, Enniskillen.
Two of the victims were declared dead at the scene on Wednesday morning and a third died later in hospital.
A man – who is a member of the same household – is being treated for serious gunshot injuries at the Royal Victoria Hospital in Belfast.
Police said no arrests had been made and it was not anticipated that any would be made.
They added that the investigation was at an early stage, but a suspected triple murder and attempted suicide was one line of inquiry for detectives.