The violent scene took place Monday in a rural area on the Costa Blanca, close to the town of Elche, the regional police service said in a statement to AFP.
The police declined to reveal to AFP the nationalities of the two people killed or of the suspects who were arrested Tuesday.
But El País said the two fatalities were German, and the two suspects were Polish, with the latter being arrested inside a house.
The arrested have been described in the Spanish press as okupas, squatters.
El País also said a third person of unknown nationality was believed to have been badly hurt in the fight.
The police did not confirm whether there was a third casualty, saying they had to respect the confidentiality of the investigation.
El País said the two people killed and the third person hurt had tried to evict the two Polish suspects from a house they had been occupying for the past four days, leading to the confrontation.