The cabinet said any action will be delayed until a third soldier who is believed captured has been recovered, Channel 10 Television reported.
Israel earlier on Sunday sent tanks and troops into the Gaza Strip hours after a Palestinian attack against an army border post that caused Israeli and Palestinian casualties.
The decision came at the urging of Ehud Olmert, the prime minister, the privately owned channel said, citing a politician it did not name. It said Olmert was determined that the life of the soldier seized from an army post at the Gaza border should come first.
But ministers gave their approval in principle to a phased series of operations in the Gaza Strip later, the channel said.
Olmert earlier said he held Mahmoud Abbas, the Palestinian president, and the Hamas government responsible, while a senior cabinet minister said Israel would "take out" Palestinians involved in attacks.
"Israel sees the Palestinian Authority, headed by Abu Mazen [Abbas] and the Palestinian government responsible for this incident," Olmert said at the weekly cabinet meeting.
Israel earlier sent in troops and
tanks to the Gaza Strip
Several Palestinian armed groups claimed responsibility for the attack on the post on the border between southern Gaza and Israel, including the Popular Resistance Committees and the armed wing of the ruling Hamas movement, the Izz al-Din al-Qassam Brigades.
Benjamin Ben Eliezer, the Israeli infrastructure minister, called the Palestinian attack "very serious" and said it was an "escalation" in the situation along the already volatile border.
"We need to examine all the possibilities because the terrorists infiltrated Israeli territory," he said.
Dan Halutz, the Israeli army chief, held a meeting to weigh the military response and their recommendations will be presented to Olmert later in the day.