Defense Minister Shaul Mofaz gave the order after consulting with his security chiefs, the official said on condition of anonymity because he is not authorized to report on the contents of the meeting.
The defense minister ordered a "crushing" blow on Gaza, CBS News correspondent Robert Berger reports.
The forces would concentrate opposite northern Gaza, from which 21 rockets were fired at Israeli border towns overnight, the official said.
Israel Radio said Mofaz also decided to continue targeting Hamas militants from the air.
In a first response Saturday, Israel fired missiles at several suspected Hamas weapons workshops in Gaza and sealed the West Bank and Gaza.
The overnight rocket barrage was the first since Israel pulled out of Gaza nearly two weeks ago. Israel has said it will display "zero tolerance" for attacks on its towns after the withdrawal.
There were no immediate reports of casualties from any of the blasts.
The air strikes, which Israeli said targeted militant weapons facilities, came after Gaza militants launched 21 homemade rockets into the Israeli town of Sderot, injuring five Israelis, one moderately and the rest lightly, the army said.
A total of 30 homemade rockets were launched from Gaza into Israel since Friday afternoon.
Islamic Jihad claimed responsibility for the first wave of rockets, saying they were launched in retaliation for an Israeli raid near the West Bank town of Tulkarem that killed three Islamic Jihad militants.
Hamas claimed responsibility for many of the rockets launched toward Sderot overnight.
Hamas blamed Israel for a blast that killed 15 people Friday evening at a rally in the northern Gaza refugee camp of Jebaliya and threatened to retaliate.
Israeli denied involvement in that blast and Palestinian security forces said it was caused by the militants' mishandling of explosives.
The Israeli army said the air strikes targeted three Hamas weapons facilities, a weapons warehouse in the Jebaliya refugee camp in northern Gaza, a weapons factory in Gaza City and another weapons warehouse in Gaza City.
One missile landed in an empty field near an abandoned workshop where militants used to make homemade rockets in Gaza City, causing no damage or casualties, according to Palestinian officials. The second hit a garage outside the house of a Hamas fighter. It was not immediately clear if there were casualties in that attack.
Before leaving Gaza last week, Israeli officials said they would deal harshly with any attacks originating from the volatile coastal strip.