They said the operation was necessary to stop Palestinian fighters smuggling in weapons from Egypt.
Eli Yishai, the Israeli industry and trade minister, told reporters on Sunday: "Action must be taken without hesitation. Any hesitation is dangerous and we must act immediately.
"When we left the Philadelphi corridor, I said that abandoning it is a doorway to hell."
The Philadelphi corridor is the Israeli term for the 12km-long border zone.
Yishai's call to move back into the corridor, a year after Israel pulled troops and settlers out of the Gaza Strip, was echoed by two other cabinet ministers and a senior commander of military forces in the area.
Ghazi Hamad, a Palestinian government spokesman, denounced the proposal as a potential ruse for an Israeli reoccupation of Gaza.
He said: "The call to retake the border is a serious escalation and an incitement for more Israeli aggression."
Israel claims that tonnes of munitions, including advanced shoulder-fired missiles, have been smuggled from Egypt in a network of underground tunnels since their withdrawal from Gaza.
The Israeli military is still reeling from its failure to defeat well-armed Hezbollah fighters during the recent Lebanon war, and has struggled to stop cross-border rocket fire by Gazan fighters.
Yom-Tov Samia, a reservist major-general on special assignment as deputy chief of the Southern Command, called for the Gaza border corridor to be retaken and its buffer zone widened - something that may entail razing Palestinian homes.
He told Israel's Army Radio: "The objective would be to prevent Hamas from replicating what happened with Hezbollah in Lebanon.
"This would have to take place in the coming days or weeks."
Ehud Olmert, the Israeli prime minister, was expected to convene senior ministers on Tuesday or Wednesday to discuss the option of a major anti-smuggling operation in Gaza, political sources said.
But the sources said that it was unlikely that any such mission, which would strain Israel's strategic ties with Egypt, would go ahead before a planned trip by Olmert to the US in mid-November.