The nomination of Ran Baratz, founding editor of a conservative news site, has sparked an uproar in Israel. Netanyahu said he had been unaware of the comments.
Baratz recently said on his Facebook page that US resident Barack Obama's response to Netanyahu's speech to Congress this year was an example of "modern anti-Semitism in liberal Western states."
Netanyahu's speech marked a low point in relations between the two leaders. Obama skipped the speech, which sought to persuade US lawmakers to vote against a deal on Iran's nuclear program.
In a 2004 column, Baratz, who lives in a West Bank settlement, voiced support for Jewish extremists pushing for a greater Jewish presence at a Jerusalem holy site.
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Israel is currently wracked by a wave of violence fueled by Palestinian allegations that Israel is plotting to take over the holy site. Israel denies the allegations.
Much of the furor has centered on a Facebook post Baratz made about Israel's largely ceremonial but much-admired President Reuven Rivlin.
"This is the man the prime minister chose to be my mouthpiece, all of our mouthpieces, to talk to the world in our names. This man, with his words dripping with poison, his mouth is our mouth now," wrote satirist Mika Almog in the Yediot Ahronot daily.
A statement from Netanyahu's office called the posts "inappropriate," saying Baratz would show restraint once in public office.