The incident, hours after Egypt's Muslim Brotherhood declared victory in the country's presidential election, raised Israeli concern about lawlessness in Egypt's Sinai desert since the fall of Hosni Mubarak in 2011.
"We can see a disturbing deterioration in Egypt's control of the Sinai's security," Israeli Defense Minister Ehud Barak said, commenting on the attack, Reuters reports.
"We are waiting for the election results. Whoever wins, we expect him to take responsibility over all of Egypt's international commitments," he told reporters in a reference to a 1979 peace treaty with Israel.
Israeli military spokesman Yoav Mordechai said "a terrorist squad opened fire and possibly also fired an anti-tank rocket at an area where (Israel) is constructing the border fence".
An Israeli military source said one of the workmen, an Arab citizen of Israel, was killed by the gunmen. There was no immediate claim of responsibility for the attack, about 30 kilometers (18 miles) from the Gaza Strip.
Soldiers who rushed to the scene killed two of the militants and searched the Israeli side of the border for more gunmen, the source said.
To curb an influx of African migrants and boost security, Israel is building a fence along the frontier with Egypt that it hopes to complete by the end of the year. The barrier will run most of the 266 km (165 miles) from Eilat, on the Red Sea, up to the Gaza Strip.
In the most serious attack in the area since the Egyptian popular uprising, militants crossed over the Egyptian border and killed eight Israelis in August 2011.
On Saturday, at least two rockets were fired deep into southern Israel, causing no damage or casualties. It was not clear whether they were launched from Gaza or Sinai.
Palestinian militants in the Gaza Strip, ruled by Islamist Hamas, have launched Grad rockets at Israel from the coastal territory in the past. Israel says militants have also crossed into Sinai to launch similar attacks on its territory.
Overnight on Sunday, Israeli aircraft carried out a series of strikes in the Gaza Strip in response to rocket fire from the enclave. Medical sources in Gaza said seven people were wounded.
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