In a statement, Ashraf al-Qidra, a spokesman for Gaza's Health Ministry, said that one of the two martyrs -- neither of whom has yet been identified -- was a minor.
According to al-Qidra, "dozens" of Palestinian protesters were affected by teargas while 18 others sustained gunshot injuries.
Demonstrators demand the "right of return" to their homes and villages in historical Palestine from which they were driven in 1948 to make way for the new state of Israel.
They also demand an end to Israel's 11-year blockade of the Gaza Strip, which has gutted the coastal enclave's economy and deprived its two million inhabitants of many basic commodities.
According to the Health Ministry, more than 190 Palestinians have been martyred -- and 20,000 others injured -- since the rallies first began on March 30.
