An Israeli military spokeswoman said its aircraft on Wednesday fired at two men who had approached the frontier carrying rifles.
Palestinian security forces said the men belonged to al-Aqsa Martyrs Brigades and were on their way to plant bombs.
Al-Aqsa Martyrs Brigades has carried out dozens of rocket attacks against Israel.
The Palestinian government, which the Islamist group Hamas took over after winning a January election, said Israel’s recent attacks in Gaza were aimed at strangling the new administration.
Israel, the United States and the European Union have cut direct aid to the Palestinian Authority since Hamas’s election victory and have urged it to renounce violence and recognise the Jewish state and interim Israeli-Palestinian peace deals.
In a statement, the Hamas cabinet called the EU action collective punishment and a “green light to the Israeli occupation to continue its aggression against the Palestinian people”.
Israel has increased airstrikes and shelling of Gaza in what it says is a response to fighters firing rockets into Israel. The army has intensified the shelling since a Palestinian bomber killed four Israelis in the West Bank last month.
The Israeli army killed a Palestinian girl and wounded 12 others, including five children, on Monday when an artillery shell hit a house in northern Gaza.