The shooting took place in the city of Setubal where the pigeon race was, around 50 km (30 miles) south of the capital, Lisbon.
Local media reports that the feud was related to homing pigeons and an illegal vegetable garden.
The victims were reportedly participating in a pigeon racing competition when they were killed.
CNN Portugal reported that the 66-year-old suspect killed himself when police arrived on Sunday morning.
Setubal police commissioner Andreia Gonçalves described the deaths as “an isolated situation” related to an unresolved issue between the men.
A source in the Judiciary Police told the Publico news site that the disagreement related to the breeding of the pigeons.
The identities of the suspect and victims have not yet been revealed. The gunman reportedly lived in a tent in Setubal.
A police investigation is underway.
Portugal has restrictive gun laws but firearms are legal for hunting.
