Israeli troops opened fire at a group of suspects along the Egyptian border on Tuesday, two of whom had crossed from Egypt, a military spokesman said, indicating that several of them were wounded.
The incident took place 2:00 pm (1200 GMT), the army said.
Also during the afternoon, Israeli Prime Minister Benjamin Netanyahu paid a visit to another area of the Sinai border to examine the ongoing construction of a vast barrier along the frontier to halt the influx of smugglers and immigrants, his office said, without specifying at what time he was there.
"During a routine patrol along the Israel-Egypt border, the force identified two suspects driving ATVs (all-terrain vehicles) from Israeli territory towards Egypt," the spokesman said.
"At the same time, two infiltrators crossed from Egypt into Israel."
The soldiers fired warning shots, then fired towards the legs of the four suspects, hitting two of them, he said.
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"The infiltrators then crossed back into Egypt along with one of the two from the Israeli side," he told AFP, saying one had driven over the border on his quad bike.
Once they crossed the border, there was "an exchange of fire with Egyptian security forces," he said.
The fourth man, who remained on the Israeli side on his quad bike, promptly drove off and troops had set up roadblocks in a bid to find him, the spokesman said.
According to an Israeli security source, two of the three who crossed into Egypt were killed in the exchange of fire. It was not clear what happened to the third.
"We assume this was probably some sort of smuggling attempt," the source said, indicating there was no immediate information on any of their identities.
Border security incidents have increased in recent months and Israel has warned that lawlessness in post-revolution Egypt has led to an increase in smuggling as well as attempts by militants to exploit the Sinai to stage attacks against the Jewish state.
In a bid to prevent such incidents, Israel is building a giant steel security barrier along the frontier, which is due to be completed by the end of this year.