The 20-year-old man from Gaza was seriously wounded by gunfire during clashes at the border on Friday.
A Gazan died on Saturday after being wounded by Israeli fire during a protest on the border over US recognition of Jerusalem as Israel's capital, a Palestinian health official said.
Jamal Muslih, 20, of Al-Bureij refugee camp in central Gaza, had been seriously wounded by live fire on Friday, health ministry spokesman Ashraf al-Qudra said.
His death brings to 13 the number of Palestinians killed since US President Donald Trump announced on December 6 that he would recognise Jerusalem as Israel's capital and move the US embassy there from Tel Aviv.
Eleven protesters died after clashes with Israeli troops, and two others were killed in an Israeli air strike on Gaza earlier in the month.
More than 50 Palestinians were wounded in the Friday clashes on the Gaza-Israel border as part of a "day of rage" over the US declaration, called for by both Gaza rulers Hamas and fellow militant group Islamic Jihad.
In the occupied West Bank, the Palestinian health ministry said at least 16 people were wounded when Israeli troops fired live rounds during demonstrations, while others were hit with rubber-coated bullets.
Earlier on Friday, militants in Gaza fired three rockets at southern Israel, two of which were intercepted by the Iron Dome aerial defence system, with the third hitting a village near the border, causing damage but no casualties.
Israeli aircraft and tanks targeted two Hamas positions near the border in response, again causing damage but no casualties.
Rockets from Gaza are often fired by fringe Islamist groups but Israel holds Hamas responsible for all attacks from the territory.