The measure was agreed by a security cabinet meeting following the temporary breach of the Gaza-Egypt border, when thousands left Gaza unchecked.
Plans for a fence were dropped years ago because the multi-million dollar price tag was deemed too expensive.
Israel was struck by its first suicide bombing for more than a year on Monday.
Initial speculation that the assailants were Gazans who arrived via the largely unguarded 230km (150-mile) Egyptian border was quashed on Tuesday when Hamas movement said the attackers had come from the occupied West Bank.
Israeli officials were quoted saying that because of the mountainous terrain, the fence would not extend along the entire border but sensors would protect the gaps.
The budget for the construction has not been decided yet, nor where the money would come from, the officials said.
Children wounded
Israel launched further air strikes against Gaza on Wednesday, targeting militants firing rockets at its territory.
One of the unguided rockets landed near a house in a communal farm near Gaza, causing shrapnel wounds to two children, aged two and four.
Hamas claimed responsibility for the rocket fire which struck the Kibbutz Beeri.
Earlier, four members of Hamas, which has been in control of Gaza since June, were reported to have been wounded in the north of the Gaza Strip.
On Tuesday, at least seven people were killed in an Israeli air attack on a Hamas-run police station in Gaza.
The suicide attack in the remote southern Israeli town of Dimona on Monday, in which a woman and two bombers died, would be Hamas's first inside Israel since 2004.
On Sunday, Egyptian forces finally resealed the Gaza border, nearly two weeks after its Israeli-built barriers had been blown apart by militants.
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