The initial attack and retaliatory strikes were followed Saturday night by the firing of dozens of rockets into Israel from the Strip, Ynetnews reported.
The Israeli military said its aircraft hit a terrorist cell preparing to fire rockets. Palestinians sources in Gaza said one man was killed and another man was injured, Ynetnews said.
The Israeli news website reported the four Israeli troops were injured when their vehicle was hit by an anti-tank missile while patrolling near Karni crossing. Two of the wounded soldiers were in serious condition and the other two were in moderate condition.
Ynetnews said the Abu Ali Mustafa Brigades claimed responsibility for the attack, though the Israeli military suspected Islamic Jihad militants were to blame. Ynetnews said the Al-Arabiya network later reported the Izz al-Din al-Qassam Brigades claimed responsibility.
Ynetnews said its Gaza medical sources reported Israel's retaliatory shelling produced four fatalities and 25 civilian casualties, including children.
"An anti-tank missile was fired at an IDF [Israeli Defense Forces unit] ... on routine patrol near the security fence in northern Gaza Strip,' the Israeli military said in a statement. "Four soldiers were wounded as a result. IDF forces returned fire.
"The Hamas terror group is responsible for any such acts."
The Israeli Defense Ministry ordered the temporary closing of the Kerem Shalom crossing, the key passageway for goods to the Gaza Strip, following the attack.