Military spokesman Arye Shalicar said the way the man was dressed "allowed him to approach the soldier".
The foreign ministry distributed photos of a man said to be the attacker wearing a shirt with the word "press" stamped on it and a fluorescent yellow vest.
In another unverified photo posted online, he is seen attacking a soldier with a knife.
The Foreign Press Association in Israel condemned the attack, calling it a "violation of press privilege."
Thirty-five Palestinians have been killed, including alleged attackers, since October 1.
Hundreds more have been wounded in clashes with Israeli forces.
Seven Israelis have been killed and dozens wounded in a series of gun, knife and car attacks.
The incident occurred after Palestinians called for a "Friday of revolution" against Israel amid a wave of deadly unrest.
There were protests in a number of areas of the West Bank, with people taking to the streets in Hebron, Bethlehem and elsewhere. Clashes also broke out in the Gaza Strip, where a Palestinian was killed by Israeli fire.
Overnight Palestinians torched Joseph's Tomb, a site revered by Jews in the West Bank in an incident that threatened to further inflame passions.
Palestinian president Mahmud Abbas, under pressure over recent comments that some have labelled incitement, quickly condemned the fire at the site in the northern city of Nablus. He said that attack "offends our culture, our religion and our morals."
The United Nations Security Council will hold an emergency meeting at Jordan's request on Friday to discuss the upsurge of violence.
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