"I am still in favour of pardoning Private Azaria," Netanyahu told reporters accompanying him on an official visit to Australia, Israel's Channel 10 said.
Netanyahu had already spoken out in favour of such a pardon even before the sentence.
After months of an exceptional trial that captivated Israel and highlighted deep divisions in public opinion, an Israeli military court on Tuesday sentenced Elor Azaria to 18 months in prison, with a further 18 months suspended.
The March 2016 shooting in the occupied West Bank city of Hebron was caught on video by a rights group and spread widely online.
It showed Sharif, 21, lying wounded on the ground, shot along with another Palestinian after stabbing and wounding a soldier, according to the army.
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Azaria then shoots him in the head without any apparent provocation.
Many Israelis sympathise with Azaria, who reportedly said the attacker "needed to die."
A number of ministers in the government, considered the most right-wing in Israel's history, have called for him to be pardoned.
Military leaders, however, have said the conviction is important for the institution's reputation.
A poll published Wednesday by the Maariv daily found 69 percent of Israelis support a pardon, with 56 percent saying the punishment was too severe.
In Australia, Netanyahu expressed concern about the potential impact of the trial on soldiers facing violence who might hesitate to fire for fear of investigation, public radio reported.