"The Al-Jazeera channel continues to incite violence around the Temple Mount," Netanyahu wrote in a Facebook post, referring to the Haram al-Sharif compound in Jerusalem, known to Jews as the Temple Mount.
"I have appealed to law enforcement agencies several times to close the Al-Jazeera office in Jerusalem. If this is not possible because of legal interpretation, I am going to seek to have the necessary legislation adopted to expel Al-Jazeera from Israel."
Israel has regularly accused Al-Jazeera of bias in its coverage of the Israeli-Palestinian conflict.
The network did not immediately respond to a request for comment. A spokesman for Netanyahu also did not respond to a request for further comment on the post.
Protests and deadly unrest have erupted in the days since new security measures were installed at the holy site.
A tense standoff was still underway between Israel and Muslim worshippers at the Jerusalem holy site despite the removal of metal detectors and other installations there, with concerns the situation could deteriorate into major unrest.
Muslims have refused to enter the site and have prayed in the streets outside for more than a week after Israel installed the new security measures at the compound.
The Israeli measures followed an attack that killed two policemen on July 14.
Palestinians view the security move as Israel asserting further control over the site, which houses the revered Al-Aqsa mosque and the Dome of the Rock.
Regional kingpin Saudi Arabia, Bahrain, the United Arab Emirates and Egypt broke ties with Qatar on June 5, accusing it of fostering extremism and later issuing 13 demands, including Al-Jazeera's closure.
Netanyahu has sought to improve ties with countries in the region, where it is heavily criticised over its 50-year occupation of Palestinian territory.
Egypt and Jordan are currently the only two Arab countries with peace treaties with Israel.
The prime minister has also faced backlash among Israelis for his decision to install the metal detectors after the attack at such an ultra-sensitive site, with many calling it a miscalculation that he was forced to back down from.
Netanyahu heads what is seen as the most right-wing government in Israeli history.
He has frequently criticised the news media, accusing it of seeking to undermine his government.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)