TEL AVIV (CNN) -- Israeli tanks, helicopters and ground forces have crossed into southern Gaza after Palestinian militants tunneled under the border and attacked several army posts, killing two soldiers and capturing a third, according to the Israeli army.

The Israeli army "will do everything that is required" to bring the missing soldier back to Israel, army chief of staff Dan Halutz said at a news conference.

When asked if Palestinian President Mahmoud Abbas was helping to negotiate his release, Halutz said he did not know.

However, Palestinian sources are saying that Abbas is involved in talks with militants to gain the soldier's release. The Egyptians are mediating the discussions, the sources said.

Ghazi Hamad, a spokesman for the Palestinian Cabinet, said the Palestinian government -- while still trying to confirm details about the incident -- was trying to resolve the kidnapping issue diplomatically, via the president, the Egyptians and others. He asked Palestinian factions to keep the soldier alive and "deal with him" in a "good way." Hamad said the Palestinian government is asking Israel not to resort to a "military escalation" and avoid making the situation more complicated."

On Sunday morning, a group of about seven militants emerged from a tunnel inside Israeli territory near the Gaza-Israel-Egypt border and attacked the military posts, Israeli security sources said.

The militants tossed hand grenades at an Israeli tank near the Sufa Crossing, killing the two soldiers, the sources said.

They also fired an anti-tank missile at the army post, prompting a gun battle that left two militants dead, according to the Israel Defense Forces.

Palestinian security sources said three militants were killed in the attack.

About an hour later, an explosion went off in the same area, injuring two soldiers -- none seriously -- Israeli security sources said.

Another soldier was wounded in the melee, according to an Israeli hospital spokesman.

An Israeli community just north of the army post was closed down and residents in the area were called to stay in their houses, the Israeli sources said.

The militants who survived the attack escaped back into Gaza, and Israeli forces crossed the border to search for them, the Israeli army said.

The army said they deployed limited forces in the area where the tunnel was dug to search for the militants, but not part of an offensive operation.

Israel Radio reported that Israeli tanks, armored vehicles and bulldozers -- backed by helicopters -- were involved in the raid near the site of the attack.

Palestinian security sources said three Palestinian militant groups claimed responsibility for the attack: Izzedine Al Qassam Brigades, which is the military wing of Hamas; the Popular Resistance Committees, an umbrella group that includes militants from Fatah, Islamic Jihad and Hamas; and an unknown group called the Army of Islam.