Israeli defense officials said they targeted a building used by terrorists in Rafah. Palestinian sources told Ynetnews.com three people were killed in the strike.
Earlier, the Hamas interior minister had ordered the group's Gaza headquarters evacuated in anticipation of the strike, Ynetnews.com said.
Seven Israelis were killed in a three-stage terror attack on roads near Eilat and the Egyptian border, army and police officials said. Six were civilians and one was a soldier, Ynet reported.
Two people were seriously injured by gunfire near the site of the attacks during a news conference by Israeli Defense Minister Ehud Barack and military chief Benny Gantz, Haaretz said.
Israeli emergency services said two women and five men were killed in the attack and at least 30 were injured, Israel Radio reported. Details of where all the fatalities occurred were not published.
Israel's Channel 10 said security officials estimate some 20 terrorists wearing Egyptian military uniforms participated in the attacks on roads near Egypt's border. Elite army and police units killed seven terrorists and sappers were checking the bodies of two believed to be rigged with explosives, the television said.
Towards nightfall security forces were still scouring the area. It was unclear whether the terrorists remained in Israel or had fled, the television report said. Roads leading to and from Eilat were sealed off.
Prime Minister Binyamin Netanyahu had warned Israel would respond. Calling the incident grave, Netanyahu said: "Israelis were harmed and Israel's sovereignty was violated. We will respond accordingly."
Barak said the army will hunt down the terrorists who waged the attacks along Israel's border.
"We are talking about a serious situation which reflects the weakening of Egypt's control in Sinai," Maariv quoted him saying. Barak said the terrorists came from the Gaza Strip and infiltrated into Israel from the Sinai.
Hamas denied responsibility for the attack and warned it would respond harshly if Israel attacks Gaza, the television said.
The first attack occurred at noon when terrorists sprayed an Egged bus with automatic fire as it traveled to Eilat, 18 miles away, Israel Radio said. The terrorists fled in a car and the bus driver continued to a nearby army base, alerting troops and emergency services.
Seven people were injured, Israel Radio said.
Egged spokesman Ran Ratner told Israel Radio bus No. 392 left Beersheba at 8:05 a.m. and headed for Eilat, passing military bases en route.
"The passengers were mostly soldiers heading home for the weekend," Ratner said.
Terrorists detonated a bomb near an Israeli army patrol called to the site where the bus was ambushed. The army admitted there were casualties but refused to reveal further details.
On roads near the shooting incident and the Egyptian border, terrorists detonated bombs and fired an anti-tank rocket at Israeli military and civilian vehicles, causing further casualties, the report said.
The White House Thursday released a statement on the attacks, saying: "We condemn the brutal terrorist attacks in southern Israel today in the strongest terms. Our deepest condolences go to the victims, their families and loved ones, and we wish those injured a speedy recovery. The U.S. and Israel stand united against terror and we hope that those behind this attack will be brought to justice swiftly."