It did not name the men and gave few details of the allegations against them, but said one of trio was convicted of kidnapping a boy, raping him and then killing him.
It denounced the man who helped Israel as a "traitor."
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The ministry said in a statement the families of the murder victims had refused to offer an amnesty to the killers.
The executions were carried out "in accordance with our religion, rulings of the Palestinian law and in preserving the rights of citizens and achieving the security of the community", the statement said.
Since Hamas took control of the Gaza Strip in 2007, at least 11 prisoners have been executed and more than 30 death sentences have been handed down by the courts, including to numerous people charged with helping the Israeli security forces.
Hamas refuses to recognize Israel and its charter calls for the destruction of the Jewish state.
Under local law, Palestinian President Mahmoud Abbas is meant to have the final say on whether executions should be carried out, but Hamas refuses any such consultations.
Human rights groups have repeatedly condemned the use of the death penalty in Gaza, but Hamas rejects such criticism.
"The rulings were carried out ... after the defendants had been given their full right to defend themselves," the interior ministry said.
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