Israel has been reluctant to invade Gaza because of concerns of getting bogged down there.
But Barak told his security chiefs on Thursday that an offensive was a definite option.
“The major ground operation is real and tangible. We are not afraid of it,” he said, according to a participant in the closed door meeting.
Hamas officials struck a defiant tone on Thursday.
“We will never have equipment comparable to our enemy, but we are working all the time to have enough to make any aggression a regrettable adventure for the enemy,” said Abu Obeida, a spokesman for the Hamas military wing, Izzedine al-Qassam.
The threat of a full-scale invasion came as the Israeli military continued to pound Gaza on Thursday, killing 20 Palestinians, including five children playing football.
The air strikes brought the toll to more than 30 dead and more than 60 injured in two days of attacks.
Hamas has hit Israel with more than 80 rockets in the same period.
Along with its usual Qassam rockets that have a short range, Gaza fighters fired Iranian-made Grad rockets at Ashkelon, 17km north of Gaza.
One hit an apartment building, slicing through three floors and another landed near a school, wounding a 17-year-old girl.
The latest round of rocket fire was the most intense so far, and Uri Bar-Lev, the police chief, said it was the first time a building in Ashkelon was hit.
That pushed Ashkelon residents to demand better protection and Barak pledged to install a warning system within hours, defence officials said.
In Tokyo on Thursday, Rice briefly met Ehud Olmert, the Israeli prime minister, and said the Hamas rocket attacks “need to stop”.
She also expressed concern for the humanitarian situation in Gaza, which is suffering shortages of certain basic goods due to a blockade imposed by Israel, and urged calm on all sides.
Rice is expected to visit the Middle East next week to help push peace efforts forward.
Nabil Abu Rdainah, a spokesman for Mahmoud Abbas, the Palestinian president, who is negotiating with Israel, said in a statement its military actions “meant only one thing: the Israeli government … aims to destroy the peace process”.
Olmert said at the end of a four-day visit to Japan that “the continuous shooting of Qassam rockets against uninvolved, innocent civilians is a major threat to the stability” of Israel‘s political contacts with Abbas’s Palestinian Authority.
He said, however, that he planned to hold another of his regular meetings with Abbas within the next two weeks.