Adham Amara, 17, died at a protest camp in Gaza City, while Tamer Abu el-Khair, also 17, died in hospital after being shot in the southern city of Khan Younis, authorities said.
Another teenager Belal al-Najjar, 17, was also shot dead at a protest location, the ministry said.
Their deaths came hours after Mohammed Saad, 21, was killed during skirmishes overnight as tens of thousands of Palestinians mark a year of weekly demonstrations on the border.
A Gaza hospital worker said Mr Saad was a member of the so-called “night disturbance unit”, which routinely burns tyres, flashes laser lights and detonates explosives to distract soldiers and disturb residents of Israeli communities.
Sixty-four other protesters have reportedly been injured in Israeli gunfire today.
The marches are calling for an end to an Israeli-Egyptian blockade, which was imposed when Hamas took over Gaza by force in 2007.
The Israeli army, which has tanks and mobile artillery guns stationed near the fence, says 40,000 Palestinians have gathered for the protest.
The demonstrators have responded to Hamas’ calls for a large participation.
Dozens are reported to have approached the fence, unfurling Palestinian flags and throwing rocks and explosives towards Israeli troops.
The soldiers reportedly responded with tear gas and live fire.
The Israeli military said in a statement on Saturday: “The rioters are hurling rocks and setting tyres on fire.
“In addition, a number of grenades and explosive devices have been hurled at the Gaza Strip security fence.”
Gaza’s Hamas rulers pledged to keep the crowds a safe distance from the fence as Egyptian mediators tried to cement a ceasefire agreement.
Dozens of volunteers in fluorescent vests were deployed to restrain demonstrators, and ambulances have lined up in front of clinics as police supervise encampments erected far from the fence.
The protests have come at a sensitive time for Israel and Hamas.
Israeli prime minister Benjamin Netanyahu is seeking his fourth consecutive term in the next election on 9 April, but is facing a serious challenge from a group of former army chiefs who have criticised what they say is his failed Gaza policy.
He is likely to want to keep the border quiet in the final stretch of his campaign, without seeming to make concessions to Hamas.
Mr Netanyahu took heavy criticism this week for what was seen as a soft response to renewed rocket fire out of Gaza.
Hamas faces growing unrest in Gaza as a result of worsening conditions after more than a decade of Israeli and Egyptian border closures.
A 12-year blockade has devastated Gaza’s economy.
Unemployment is higher than 50%, ground water has become undrinkable and electricity has turned into an intermittent luxury.
Egypt, which has repeatedly tried to broker a ceasefire between Israel and Hamas, has stepped up efforts in recent days after a Gaza rocket struck a house in central Israel earlier this week.
Palestinians with knowledge of the talks have said that Gaza protesters were required to keep away from the fence and Israeli troops were to show restraint.
Israel was to offer economic incentives for Gaza in exchange for calm under the Egyptian plan, according to Palestinian officials.
According to a Gaza rights group, 196 Palestinians have been killed in the demonstrations over the past year, including 41 minors, and thousands were wounded by live fire.
One Israeli soldier is reported to have been killed.
Two-thirds of Gaza’s two million people are refugees or descendants of refugees who fled or were forced from their homes during the war surrounding Israel’s establishment in 1948.