Ali al-Ashqar, 17, was shot in the neck along the border fence east of Jabalia in northern Gaza, a health ministry spokesman told AFP.
A second teenager was shot in the stomach east of Gaza City, the spokesman said, later identifying him as Khaled al-Rabaee, 14.
Contacted by AFP, the Israeli army declined to comment on the circumstances surrounding either of the deaths.
But in a statement, it said an estimated 6,200 "rioters and demonstrators" had gathered in locations along the border and thrown "fire bombs and explosive devices" at troops, as well as approaching the fence.
Palestinians have been holding weekly protests along the fortified border fence since March 2018.
The protesters are calling for Israel to end its crippling siege on the coastal enclave as well as demanding the right to return to lands their families fled in 1948, which are now inside Israel.
Gaza's Hamas-run health ministry spokesman Ashraf al-Qudra said a further 46 people were wounded by Israeli gunfire on Friday. Israel says any such return would mean its end as a Jewish state and accuses Gaza's Islamist rulers Hamas of using the protests as cover for attacks.
United Nations envoy Nickolay Mladenov called the killing of the two teenagers "appalling".
"Israel must calibrate its use of force," he wrote on Twitter, calling on protesters to "be peaceful" and for an end to "the cycle of violence".
At least 308 Palestinians have been killed by Israeli fire in Gaza since the protests began, the majority during the demonstrations.
Seven Israelis have been killed. The protests have calmed in recent months. Israel and Hamas have fought three wars since 2008.
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