It was not immediately clear what they were doing near the border, but an Israeli military spokeswoman said Saturday night the army had opened fire on two men who were spotted moving suspiciously toward a frontier "no-go" zone. The two were identified as Salah Abu Attwa and Imad Faraj, both 17.
"An army force spotted two suspects moving toward the border fence and opened fire," a spokeswoman said. "The two were seen to have been hit."
At the time Palestinian officials had no reports of casualties.
Soldiers were on high alert Saturday after a day of fierce cross-border exchanges in which Gaza militants fired dozens of shells into Israel, wounding two people, and Israel pounded Gaza in return, injuring at least five Palestinians and cutting power supplies.
Overnight Palestinians fired a rocket into Israel but it fell on open ground, causing no casualties or damage, the military said on Sunday.
Militants also fired a missile at an Israeli tank alongside the border fence but the projectile was destroyed by the army's newly deployed Trophy anti-missile system.
The tank crew returned fire but it was not known if anyone was hit.
Israel routinely responds to rocket and mortar fire with air raids on Gaza.
It carried out a 22-day offensive, codenamed "Operation Cast Lead" against Gaza rocket fire in December 2008 and January 2009, in which 1,400 Palestinians died, more than half of whom were civilians, and 13 Israelis, 10 of them soldiers.