The Israeli military launched its incursion into Rafah in early May despite international objections over the fate of Palestinian civilians sheltering there.
A strike over the weekend that started a fire and killed dozens in a displacement camp drew a wave of fresh condemnation, including a social media campaign with the slogan "All eyes on Rafah" that has been shared by tens of millions of users.
Israel, which has repeatedly vowed to destroy “Hamas” after the Palestinian militant group attacked southern Israel on October 7, said on Wednesday its forces had taken over the 14-kilometre (8.5-mile) Philadelphi corridor on the Gaza-Egypt border, which it suspects was used for weapons smuggling.
Military spokesman Rear Admiral Daniel Hagari announced Israel had taken "operational control" of the narrow border area, where he said troops had "discovered around 20 tunnels".
Egypt, a longtime mediator in the conflict which has become increasingly vocal in its criticism of the Israeli operation, has rejected claims of smuggling tunnels running beneath the buffer zone.
"Israel is using these allegations to justify continuing the operation on the Palestinian city of Rafah and prolonging the war for political purposes," a high-level Egyptian source was quoted as saying by state-linked Al-Qahera News.
Egyptian officials have said a potential Israeli takeover of Philadelphi could violate the two countries' landmark 1979 peace deal, though there has been no official comment from Cairo since the military's announcement.
On a visit to Beijing, Egyptian President Abdel Fattah al-Sisi called for increased humanitarian assistance to besieged Gaza, and reiterated his country's longstanding opposition to "any attempt at forcing Palestinians to forcibly flee their land".
Chinese leader Xi Jinping, meanwhile, called on Thursday for a "broad-based, authoritative and effective international peace conference" to address the war, as he hosted Arab leaders including Sisi.
On the ground in the Gaza Strip, witnesses reported fighting in central and western Rafah. Others told AFP at least five people were killed in bombardment near an aid warehouse in east Rafah.
Nasser hospital in nearby Khan Yunis said at least "four martyrs were brought to the facility following a bombing" in west Rafah.
Witnesses also said Israeli forces had demolished several buildings in the city's eastern areas where the Israeli incursion began on May 7, initially focusing on the vital Rafah border crossing, a key entry point for humanitarian aid.