(CNN) -- A Palestinian terrorist group claimed responsibility Monday for the attack on an Israeli border fence construction site that left one worker and three attackers dead, according to a North Sinai intelligence officer.
The attack on Israel's southern border with Egypt was the work of Palestinian Islamic Jihad, according to the intelligence officer, who asked not to be identified because he was not authorized to speak to the media.
The group is an Iranian-backed militant group that calls for the destruction of Israel and creation of an Islamic state in its place.
Three armed men conducted the attack Monday morning, and all were killed by Israeli helicopter fire, the officer said. Israeli officials have said security forces killed two gunmen.
The militants targeted the construction site with a roadside bomb, an anti-tank missile and small arms fire, the Israel Defense Forces said.
An Arab-Israeli construction worker died in the attack, the IDF said. Authorities identified the worker killed as Saeed Phashpashe, a father of four from Haifa.
In another attack, a rocket fired from Gaza exploded at Israel's Hof Ashkelon regional council offices, police spokesman Micky Rosenfeld said. No injuries were reported. It was not immediately known who was responsible for that attack.
The IDF also said the Israel Air Force had scored a direct hit Monday on "a terrorist squad attempting to fire a rocket at Israel from the northern Gaza Strip."
The Israeli government said Saturday that militants operating from Egypt had launched two medium-range rockets that landed near an airport construction site. No injuries were reported.
The Haaretz newspaper in Israel quoted an unnamed Israeli official as saying the Saturday attack was carried out at the behest of Egypt's Muslim Brotherhood by Bedouin in the Sinai who had been supplied by Hamas.
Gen. Saleh Al Masry, the head of North Sinai Security, told CNN that it is possible the rockets may have been fired from Sinai by Bedouin but the involvement of the Muslim Brotherhood was far-fetched.
"This attack took place on the first day of elections, and defaming the Muslim Brotherhood may have been an under-the-belt blow by Israelis to affect their ratings at the poll somehow," he said.
The security vacuum in Sinai remains one of the major challenges to the Egyptian government and its new president.
Bedouin tribes have kidnapped a number of tourists in the past months, seeking the release of fellow tribesmen detained in prison. In one case the government exchanged a Bedouin prisoner for two U.S. tourists kidnapped in Southern Sinai during their vacation.
The Israeli government and the international diplomatic community have expressed concern that Islamic extremists may have taken harbor in Sinai after the January 25 uprising that toppled Mubarak.
Usama Imam, an investigator with Egyptian National Security, expressed concern that Islamic Jihadists from Gaza have been infiltrating into Egypt through tunnels with the assistance of the Bedouin tribes.
"We are fighting armed Islamic extremists groups in Sinai like Takfir-Wal-Higra who were resurrected after the revolution and are clearly responsible for the bombings of the pipeline exporting gas to Israel," Imam told CNN
"There is increasing evidence that al Qaeda cells are present in Sinai and we are tracking them with all our security capabilities " Imam added.
Defense Minister Ehud Barak said the attacks signaled a "disturbing deterioration in Egyptian control of the Sinai."
"We are waiting for the results of the election," Barak said. "Whoever wins, we expect them to take responsibility for all of Egypt's international commitments, including the peace treaty with Israel and the security arrangements in the Sinai, swiftly putting an end to these attacks."
Militants have been launching attacks across the border with some frequency. In August 2011, militants crossed into Israel from Egyptian territory to attack civilian targets.
Eight Israeli citizens were killed in the attacks, which Israel has said were the work of a terror group based in Gaza. Responding to the attacks, Israeli troops killed five Egyptian border guards while pursuing the militants.
The incident strained relations between the two governments, with Egypt recalling its ambassador in protest.
After an investigation, Israel apologized in October for the deaths of the Egyptian policemen. A rare statement of regret was issued in the days after the shootings.
After the revolution in Egypt and the subsequent increase of instability in the nation's Sinai peninsula, the Israeli government has accelerated the pace of construction of a steel border fence that will run along the 260 kilometers (about 160 miles) of shared border.
Originally proposed as a method of stemming the flow of illegal immigration into Israel, the $350 million fence is increasingly being regarded in Israel as a necessary defense against lawlessness and what Israel says is the growing influence of radical Islamist groups operating in the Sinai Peninsula.
Construction is expected to be completed by the end of the year.
Prime Minister Benjamin Netanyahu vowed Monday that the morning attack won't slow work on the security fence.
"This barrier is meant both to prevent terrorism and also to prevent the entrance of infiltrators," he said. "Its construction is of supreme national interest."
CNN's Guy Azriel contributed to this report.