A petition signed by 110 members of the House called for the release of Ahmad Musa Mustafa Daqamseh, who is currently serving a life sentence, Ynetnews reported.
Daqamseh shot and killed the seven girls who were on a school field trip in 1997 in Naharayim, near the Israel-Jordan border.
Former Jordanian Justice Minister Hussein Mjali previously called Daqamseh a "hero," saying, "If a Jew killed Arabs, they would have built a monument in his honor."
Daqamseh told police after the shooting: "I don't know what happened to me."
"I lost control and acted," he added, saying his actions were not prompted by anyone else.