Officials from Israel, Qatar, and the USA began "intensive discussions" in Cairo on Thursday, according to Egypt's state information service.
"The mediators are also discussing ways to improve the delivery of humanitarian aid to the Gaza Strip, as part of the efforts to alleviate the population's suffering and support stability in the region," it says in a statement.
Not leaving the Philadelphia Corridor
The talks are intended to prevent a collapse of the ceasefire, whose first phase expires on Saturday. According to the agreement, the ceasefire will continue to apply while negotiations on the second phase are ongoing.
Earlier on Thursday, an Israeli official stated in a statement to the press that Israel does not intend to leave the disputed Philadelphia Corridor in southern Gaza, which constitutes a breach of the ceasefire terms.
According to the agreement, Israel was supposed to begin withdrawing from the corridor by the end of the ceasefire's first phase, which expires this weekend.
Constitutes a breach of terms
"We will not leave the Philadelphia Corridor. We will not allow Hamas murderers to move freely along our border with pick-ups and weapons," said the official, who spoke anonymously in line with Israel's military rules, according to The Times of Israel.
"And we will not allow them to rearm themselves through smuggling."
According to Israel, the strategically important corridor, along the border between Gaza and Egypt, is used by the terrorist-listed Hamas to smuggle in weapons.
Hamas responds to Israel's statement by claiming that any attempt to maintain a buffer zone in the Philadelphia Corridor constitutes "flagrant breaches" of the ceasefire terms, according to AP.