The IDF is preparing for a possible resumption of rocket fire from Gaza on Monday evening, as the current five-day ceasefire is set to expire.
The ceasefire is set to expire at midnight, but Hamas has been known to violate truces before they officially expire.
The high alert for Monday evening comes in the wake of estimates of diplomatic sources in Jerusalem that the chances of a lasting ceasefire deal before Monday night are very slim.
Earlier on Sunday, as truce talks in Cairo continued, Israel pre-empted any agreement by unilaterally offering Gaza a concession and lifting a ban on fishing in the Hamas enclave.
Gaza fishermen have been blocked from their work since July 8, during the Hamas terror war on Israel, which has included several attempts to infiltrate Israel by sea.
Nevertheless, "as a sign of goodwill, Israel has allowed fishing off the Gaza Strip up to 3 nautical miles," an Israeli government official told AFP on condition of anonymity.
Over the past eight years, Israel has set a six-nautical-mile limit for Gaza's fishermen when tensions were lower, restricting it to three miles when hostilities have escalated.
During the operation fishing was cancelled altogether due to the security threats. Besides using the sea for infiltrations by gunmen into Israeli territory, Gaza terrorists often try to smuggle weapons into the Hamas stronghold under the guise of fishing vessels.
Talks in Cairo are based on an Egyptian proposal, which reportedly was rejected by Hamas, and which puts off difficult issues such as a disarmament of Gaza and a Hamas demand for a Gaza sea and airport for a month after the truce agreement.