The statement added that Friedman is "further complicated the road towards the peace process and the resumption of negotiations between the Israeli and Palestinian sides" according to official Palestinian Authority news agency WAFA.
Three other Palestinians were wounded, one critically, it said.
"An Israeli father of six was killed last night in cold blood by Palestinian terrorists", Friedman said on Twitter on Wednesday after a 35-year-old was killed near an illegal Israeli settlement near Nablus.
In a statement, the mission said the European Union was troubled about the circumstances of the recent arrests of Palestinian minors Ahed Tamimi and Fawzi Muhammad al-Juneidi, Efe reported.
It has been the largest incidence of fire from Gaza since the 2014 Israel-Hamas war.
Strict measures have been imposed on tens of thousands of Palestinians following the killing of an Israeli rabbi in a drive-by shooting in the West Bank this week.
The killing of the Israeli settler happened on Tuesday near the illegal Israeli settlement of Havat Gilad, where the 35-year-old rabbi resided.
Around 2,000 Palestinians, enraged by US President Donald Trump's decision to move the American embassy from Tel Aviv to Jerusalem, swarmed the streets of the West Bank and Gaza for the sixth consecutive Friday, burning tires and hurling projectiles at the Israel Defense Force (IDF) in 20 locations across the occupied Palestinian territories.
The leap in the number of attacks corresponded with an uptick in terrorist activity following President Donald Trump's December 6 declaration that the United States recognizes Jerusalem as Israel's capital.
Israel's occupation of East Jerusalem effectively put the entire city under de facto Israeli control.