The remains of a Grad rocket were found on Friday evening, in a mountainous area north of the city of Eilat, the Israel Police said.
Police said they were working on the assumption that this was one of the two rockets fired from Sinai into Eilat on Wednesday, causing powerful blasts that
rocked the Red Sea resort city.
Eilat residents flooded the police's emergency number after hearing the explosions, police spokesman Micky Rosenfeld said.
No injuries or damages were reported following the explosions.
Meanwhile, an Islamist militant group operating in the Sinai Peninsula warned the Egyptian army on Wednesday that an ongoing military crackdown on jihadists in the area will force it to fight back.
The group also said Sinai jihadists had fired rockets at Israel in the
last few years. Egypt had repeatedly denied that rockets had ever been
fired from Sinai into Israel.
The Egyptian army has been hunting militants in the Sinai desert since an attack last week on Egyptian border guards that killed 16 soldiers. Egypt blamed the attack on Islamist militants.
The army operation is the biggest in almost three decades in the tense border region where troop and army vehicle movements are strictly limited under the terms of Egypt's 1979 peace treaty with Israel.
"We have never raised our weapons against the Egyptian army," the Salafi Jihadi, one of the biggest jihadist groups in the Sinai, said in a statement. "So stop the bloodshed or else you will be dragging us into a battle that is not ours," the group said, addressing the Egyptian army.
The group belonging to the Salafist jihadist current in the Sinai denied involvement in the attack on Egyptian border guards and said its true fight was with the "Zionist enemy" Israel.
Security officials had said that 20 militants were killed by the Egyptian army on the first day of the Sinai sweep on Aug. 8.
Moderates fear militant Salafists in Gaza and Sinai are joining forces, creating an environment ripe for al-Qaida were it to seek a base for use against Israel or the more moderate political Islam of Egypt's Muslim Brotherhood.
The Salafi Jihadi statement said other jihadist groups, which it did not name, were behind past attacks on Sinai's gas pipeline that delivers gas from Egypt to Israel and Jordan.