The man, who the military says is a member of Hamas, was transferred for investigation by security forces.
"2 suspects attempted to infiltrate Israel from the southern Gaza Strip and damage the (border) security fence", the army tweeted. The second infiltrator was taken away for questioning.
It later said two other infiltrators were killed after they hurled explosives at soldiers, without giving details on the locations of the two incidents.
During the most recent protests the IDF said an unusually large number of people made a "highly organized" attempt to break through the border fence, which was thwarted.More news: MS Dhoni does his daughter's hair after CSK's win over RCB
Gaza is run by the Islamist Hamas movement, which Israel and the West designate a terrorist organization.
On reports that Trump might present his Middle East peace deal, which may include financial compensation for Palestinians, Erekat said "this is morally unacceptable and Palestine is neither sold nor bought with money".
In a third incident, soldiers spotted two Palestinians trying to breach the border. According to Hamas, the attack was meant to "kill the reconciliation".
Israel's live-fire response to the protests has drawn global criticism. Israel has warned that anyone approaching the border fence is risking their lives and accused Hamas of cynically exploiting civilians for its agenda.More news: Facebook now lets parents schedule 'sleep mode' in Messenger Kids app
The protests also press for a "return" of Palestinian refugees and their descendants to what is now Israel.
The protests are to culminate May 15, the anniversary of Israel's founding.
"The deployment of snipers, careful planning and significant number of injuries to the lower limbs does reflect an apparent policy to target [those] limbs", said Omar Shakir, Israel-Palestine director at Human Rights Watch in NY. Palestinians mark the date as their "nakba", or catastrophe.More news: Ford May Be Abandoning Car Market in US
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