"Construction has begun along all towns considered to be next to the fence with Gaza," the Ynet news website reported.
It posted a video appearing to show heavy machinery operating along the border.
The defence ministry has reportedly been planning an underground structure around the Palestinian coastal enclave to prevent tunnels being dug into Israel, though the government has neither confirmed nor denied this.
According to Ynet, the barrier would have sensors to detect digging and eventually run the length of the 60-kilometre (35-mile) Gaza border.
Signup to our newsletter and follow us on Facebook and Twitter!
Gadi Yarkoni, head of Eshkol Regional Council along the border with Gaza, confirmed to AFP on Thursday that works had begun along the border, without giving any detail.
The defence ministry declined to comment.
The Islamist movement Hamas, which controls the Gaza Strip, used underground tunnels crossing the border to carry out surprise attacks in its last war with Israel in 2014.
Israel has described the tunnels as a strategic threat and Hamas has repeatedly said it is building new tunnels to be used for its defence.
Twice this year, Israel has announced the discovery of tunnels reaching across the border, with the second occasion in May leading to the worst flare-up of violence since the 2014 war.
The Gaza Strip has been under an Israeli blockade for around a decade and its border with Egypt also remains largely closed.