The troops were operating "against the terror infrastructure" in the area, the military spokesman said.
Palestinian witnesses said the Israeli forces were deployed about 400 metres inside the Gaza Strip.
Wael al-Dahduh, Al Jazeera's correspondent in Gaza, said four fighters of Izz al-Din al-Qassam Brigades, Hamas's armed wing, and two of Salah al-Din Brigades were killed on Wednesday morning in Israeli shelling.
The shelling was aimed at targets in east and south Gaza.
He said Israeli special forces had crossed the border into the Shujaiya district of east Gaza city.
Palestinian fighters taking up positions against the Israeli forces were then fired on by helicopters.
More deaths expected
Yehya Jabr, an al-Qassam Brigades field leader, was killed overnight in an Israeli air strike targeting a post in east Bureij refugee camp, in central Gaza Strip.
Medical sources said Wednesday's death toll is expected to rise as more than 10 of the injured are in critical condition.
At least one Qassam rocket was also fired from Gaza and hit the Israeli town of Sderot but caused no damage.
More than 2000 rockets and mortars were launched from Gaza in 2007, killing two Israelis.
Most of the rockets fired into Israel land in open areas, but the psychological impact of constant bombardment fuels public demands for the military to hit back.
The Israeli military conducts almost nightly air and land raids into the Gaza Strip against Palestinian fighters it alleges launch the rockets.
More than 300 Palestinians have died from these attacks over the past year.
Wednesday's raids came against the backdrop of heightened factional tensions in the heavily sanctioned Palestinian territory.
The day's other developments, Palestinian factions, with the exception of Hamas and the Islamic Jihad group, have held a meeting to discuss a number of internal Palestinian issues, particularly the containment of the crisis between Hamas and Fatah.
Mediators from Islamic Jihad and the Popular Front for the Liberation of Palestine [PFLP] on Tuesday said they had succeeded in containing two days of clashes between Hamas and Fatah fighters.
At least seven people died and up to 60 others were injured in the Gaza fighting sparked by banned celebrations of Fatah's 43rd anniversary.
A senior Hamas official admitted to Al Jazeera that its security forces had committed some excesses against Fatah supporters.
However, he insisted they were not condoned by the group and were reactions to provocative statements and a crackdown on its supporters in the West Bank.