Gaza emergency services chief Muawiya Hassanein said three Palestinian sisters, aged around 13, 8 and five, were injured by shrapnel from tank or artillery shells fired by the Israeli military toward the village of Johur Addik.
The village is located a few hundred meters from the border, east of the former Jewish settlement of Netzarim and southeast of Gaza City.
Israeli troops crossed some 200 meters into the Gaza Strip from the border and fired the shells, after Palestinians opened fire at soldiers stationed near the border fence, a military spokesman in Tel Aviv said.
Hassanein said a Palestinian was killed and another wounded when a tank fired on a group of Palestinian fighters near the border east of Gaza City.
An Israeli army spokesman said an air strike had been launched in the area where the fighter was killed, and that there had been a separate exchange of fire along the border near the refugee camp.
"Palestinians opened fire at an army patrol along the security barrier," he said. "The soldiers responded by firing in the direction of the attackers."
Earlier on Thursday, prior to the clashes, the ruling Hamas movement had said that one of its fighters had died during a "jihad mission," without elaborating. It was not immediately clear whether his death was related to the exchange of fire near the Gaza border.
Medics confirmed the man's death, but did not provide further information.
Also on Thursday, Israel security services said they had captured two Hamas men in December who had tried to infiltrate the border to capture or kill Israelis, army radio reported.
