Dubbed the "March of Return", it coincides with Land Day, when Palestinians commemorate the Israeli government's expropriation of Arab-owned land in the Galilee on March 30, 1976, and ensuing demonstrations in which six Arab Israelis were killed.
The Israeli military said thousands of Palestinians rolled burning tires and threw stones at forces stationed on the border.
Israel's Channel 2 reported that at least 20 Palestinians had received medical treatment as of noon Friday after being injured by Israeli forces.
Earlier another man was shot dead in clashes, while a farmer was killed by Israeli tank fire, according to Palestinian officials.
The reproduction of the story/photograph in any form will be liable for legal action.
Hamas has urged Palestinians to gather at the border for mass sit-ins set to last six weeks and culminate with a march to the border.
More than 200 people were hit by live fire during the clashes, the Palestinian Red Crescent said.
US President Donald Trump's recognition of the disputed city as Israel's capital in December has infuriated Palestinians, who claim its annexed eastern sector as the capital of their future state.
Maj. Gen. Eyal Zamir, commander of the Israeli military's Southern Command, which includes the border, said on Friday that "we are identifying attempts to carry out terror attacks under the camouflage of riots".
On Wednesday, Israeli tanks fired at Hamas positions in Gaza after heavy gunfire from the enclave, roadside bombs targeting border patrols and an incursion by three armed Palestinians, who penetrated some 20 kilometres into Israel before being captured.
Israeli soldiers take position next to the border fence on the Israeli side of the Israel-Gaza border, as Palestinians demonstrate on the Gaza side of the border, March 30, 2018.
The demonstrators are demanding that Palestinian refugees be allowed the right of return to towns and villages which their families fled from, or were driven out of, when the state of Israel was created in 1948. The IDF said the protesters were "rolling burning tires and hurling stones at the security fence and at IDF troops".
In Friday's incident, along with the killed Gazan, another Palestinian man was wounded.
"I was working on the next field", Samour said. Another farmer was wounded in the leg by shrapnel, Samour said.