Prosecutors were seeking to extend the remand of the soldier until April 7 in a case that has gripped the country and sparked political tensions.
The 19-year-old soldier's identity has been kept secret under a gag order, granted at the request of his lawyers.
The protesters called for the soldier's release despite video footage shared widely online showing him shoot the Palestinian in the head without any apparent provocation.
But far-right politicians have defended the soldier, and members of his family said he was being publicly "lynched" and would not receive a fair trial.
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Ex-foreign minister Avigdor Lieberman, currently a member of the opposition, was among those in court in support of the soldier.
Around a dozen of the soldiers' family members were also in the public gallery, some of them in tears.
Video of Thursday's incident in the flashpoint West Bank city of Hebron spread widely online and threatened to further inflame tensions amid a wave of violence that erupted in October.
The soldier then shoots him again, in the head, without any apparent provocation. The Palestinian, Abdul Fatah al-Sharif, was killed.
"The suspicion emanating from the investigation is that the shooting was carried out intentionally and without need," prosecutor Lieutenant Colonel Adoram Rigler told the court.
Defence lawyers said the Palestinian could have had an explosive device, even though he had reportedly been checked for a suicide belt before the shooting.
"There was no bomb-squad investigation, even if the officer kicked away the knife," said defence lawyer Ilan Katz.