Lt. Gen. Gabi Ashkenazi said that until he receives the go ahead for a broad operation, Israel would continue with its policy of airstrikes and brief ground incursions to halt Palestinian rocket attacks.
"If it is necessary, we are prepared for the possibility of action," Ashkenazi told Army Radio. "Until then I think it is our duty to exhaust all other avenues and to operate every day and night in order to provide security."
Israeli Defense Minister Ehud Barak has repeatedly said that the time for a widespread ground invasion of Gaza is drawing closer. But on Tuesday, he said now is not the time for a broad operation, which would likely result in heavy casualties to Israeli soldiers and Palestinian civilians in Gaza's crowded urban landscape.
In Wednesday's violence, Israeli tanks fired shells toward a group of Hamas militants on the outskirts of the town of Beit Lahiya in the northern Gaza Strip after dawn, Palestinian doctors and residents said. Two of the Palestinians were killed and four wounded, one critically, the doctors said.
The army confirmed the strike, saying the militants were preparing to fire mortar shells toward southern Israel.
Israel's attack on Wednesday brings to about 30 the number of militants in Gaza that Israel has killed in the past 10 days.
Israel's army frequently launches cross-border attacks and air strikes on Gaza militants, but has been unable to stop the rocket fire from the Hamas-controlled territory.
This year, Gazan militants have fired 2,000 rockets and mortars, the army spokesman said. The rockets have killed a total of 12 people in recent years and cause widespread panic in southern Israeli border towns.
Israel blames Hamas, the Islamic militant group that controls Gaza, for allowing the attacks, even though the group has not been directly involved in most of the rocket launchings.
Following its takeover of Gaza, Palestinian President Mahmoud Abbas fired the Islamic group from the government and installed a rival Western-backed administration in the West Bank. Israel formally launched peace talks with Abbas at a summit in the U.S. last week.
As part of the peace efforts, Abbas has launched a crackdown on West Bank gunmen in an effort to show Israel that he can meet Palestinian obligations to impose law and order in areas under his control.
In the West Bank city of Nablus, 13 Palestinian militants wanted by Israel surrendered to Abbas' forces a rare instance of gunmen willingly handing themselves over to Palestinian security.
Hussein Jabbour, a military intelligence official, said the men surrendered in hopes of obtaining amnesty from Israel. Several months ago, Israel offered amnesty to about 200 West Bank gunmen in exchange for them disarming and pledging not to carry out future attacks.
"This is a message to Israel that these Palestinians want peace and want (Israel) to deal with their issues," Jabbour said. He said the men were taken to a Palestinian security compound. There were no plans to turn them over to Israel. It was not clear what kind of attacks the men were involved in.
Elsewhere in the West Bank, Israeli soldiers shot and killed a Palestinian policeman during an arrest raid in Bethlehem, Palestinian officials and the Israeli military said.
A Palestinian security official said the soldiers shot at a group of policemen as they stood near a security compound.
The Israeli army said troops came under fire while trying to arrest wanted militants. The soldiers fired back and hit an armed man. Only after the firefight did the soldiers realize they had shot a policeman. The mission was aborted and the army left the area without making arrests.
Israeli and Palestinian officials are launching a joint investigation into the incident, the military said.