Nefertiti's famous painted limestone bust was stolen from Tell el-Amarna, around 300 km (185 miles) south of Cairo, in 1912 by a German archaeological mission, which shipped it to Berlin the following year.
Amarna was the short-lived capital of Nefertiti's husband, the 18th dynasty Pharaoh Akhenaten, who reigned until about 1335 B.C.
Akhenaten, called the king, was notorious for promoting the worship of the god Aten to the exclusion of Egypt's other gods. His reign also introduced a radical change in Egyptian art.
Call for signatures
In his petition launched on Saturday, Hawass asked for the return of the bust, saying it was removed from Egypt illegally after its discovery.
"We announce today that Egypt - this is the national committee, it is not a government committee - asks for the return of the bust of Nefertiti," Hawass said.
"What I need from everyone here is to go to my website... hawasszahi.com, and you will sign, one signature, to show that you would love for this bust to come back."
Hawass said he is not calling for the repatriation of artefacts taken out of Egypt legally. His campaign is focused on repatriating "three main beautiful objects" including the bust of Nefertiti, the Rosetta Stone and the Dendera Zodiac.
Officials at Berlin's Neues Museum were not immediately available for comment.
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