Donald Trump has warned Hamas to start return the bodies "quickly, or the other countries involved in this great peace will take action".
An Israeli spokesperson said the Egyptian team has been permitted to work with the ICRC to locate the bodies, and would use excavator machines and trucks for the search beyond the "yellow line".
The "yellow line" marks the boundary running along the north, south and east of Gaza that Israel withdrew to, as part of the first stage of the ceasefire deal.
Until now, Israel has not approved the entry of such teams.
Egypt, along with Qatar and Turkey, is a key signatory of the Trump-brokered Gaza peace plan, which was signed in the Egyptian resort of Sharm el-Sheikh earlier this month.
The news will be welcomed by relatives, desperate to give them a proper burial.
The ICRC has already been heavily involved in the return of hostages.
Hamas does not hand over its captives - living or deceased - directly to the Israel Defense Forces (IDF), but rather to the ICRC, which in turn escorts them through Gaza and hands them on to the IDF.
But the arrival of Egyptian excavation teams inside the Gaza Strip is new.
After more than two years of intense bombardment by Israel, the UN estimates that as much as 84% of the territory has been reduced to rubble.
Hamas says it is doing its best to retrieve hostage bodies, but it faces difficulty finding them under rubble of buildings bombed out by the Israeli military in Gaza.
It is now coordinating with the Egyptian authorities.
On Sunday, an Israeli government spokesperson said that Hamas knew where the bodies were.
"If Hamas made more of an effort, they would be able to retrieve the remains of our hostages," the spokesperson said.
Trump posted on his Truth Social platform on Saturday that action would be taken if the bodies of the deceased hostages were not returned quickly.
"Some of the bodies are hard to reach, but others they can return now and, for some reason, they are not. Perhaps it has do with their disarming," he said.
Trump added: "Let's see what they do over the next 48 hours. I am watching this very closely."