The largest demonstrations coincided with the move of the U.S. embassy in Israel from Tel Aviv to Jerusalem on Monday, which saw Israeli forces kill some 60 Palestinians, pushing the overall toll well over 100.
The death toll led to worldwide condemnations of Israel and calls for an independent investigation.
Israel has said its actions were necessary to stop mass infiltration from the blockaded Palestinian enclave run by Islamist movement Hamas. The protesters were demonstrating against the opening of the United States embassy in Jerusalem.
U.S. Ambassador Nikki Haley, meanwhile, said Hamas had stirred the violence and Israel had acted shown "restraint". His words; "This is not peaceful resistance", he said. Friday is seen as a key test of whether the current round of unrest will continue. One Israeli soldier has been wounded.
Now Hamas has used its supporters to besiege its borders with Israel to force a mass excursion into that state.
"We must strive for a future where Israel and Palestine thrive as states in which all are equally respected, and where civil society is able to play its constructive role", she said. There are no reported injuries from the strikes, to the Jerusalem Post.
Zeid said he supported the call for "an investigation that is worldwide, independent and impartial, in the hope the truth regarding these matters will lead to justice".
The Arab League held an emergency meeting of foreign ministers in Cairo, Egypt, on Thursday, to debate how to deal with the USA move and the ensuing violence in the Palestinian Territory.
Under Israel's leading general, the late Prime Minister Ariel Sharon, Israel made a decision to vacate the strip and turn it over to its Palestinian residents in 2005.
Israel has rejected criticism over Monday's violence, with the United States strongly backing its ally and blaming Hamas for the deaths. "Canada calls for an immediate independent investigation to thoroughly examine the facts on the ground - including any incitement, violence, and the excessive use of force".
The foreign ministers renewed their rejection and condemnation of Washington's recognition of Jerusalem as Israel's capital, decrying it as a blatant violation of worldwide law and related United Nations resolutions and a threat to global peace and security.
Imam Khamenei further stated that the Islamic Ummah and Muslim governments are duty-bound based on the teachings of the holy Qur'an to adopt a firm position and stand against Israeli crimes against Palestinians.
Israel accuses Hamas, with whom it has fought three wars since 2008, of seeking to use the demonstrations as cover for violence.