Both teams arrived aboard a flight from Qatar on Saturday, they added.
Egypt's state-affiliated broadcaster al-Qahera News also reported the arrival of a Hamas delegation in Cairo and cited "significant progress" in negotiations to reach the deal.
The broadcaster, citing what it termed as a high-level source, said the Egyptian security team engaged in the negotiations had reached a "consensus formula" on several contentious issues. No specific details were given.
Israel, meanwhile, is reportedly not sending a team to Cairo. A delegation will only be sent to Egypt once Hamas has responded to the current proposed ceasefire agreement, Israel's Kan radio reported on Saturday, citing a government representative.
Israel plans to send a delegation to continue indirect negotiations with Hamas if the militant organization agrees to the draft deal presented, the Israeli newspaper Haaretz quoted a high-ranking Israeli official as saying.
Israel has been bombarding the Gaza Strip from the ground and air since Hamas militants launched an unprecedented attack on Israel in October that left about 1,200 people dead.
As part of the latest mediation efforts, Hamas, which abducted some 250 people from Israel on October 7, was presented with a proposal for a ceasefire in return for the release of remaining hostages. A response is still pending.
More than 100 hostages were released during a six-day truce in November. It is unclear how many of those remaining in captivity are still alive.
As of Friday, the Hamas-controlled Health Ministry said the death toll in Gaza from Israeli attacks launched in response to the October 7 attacks stood at 34,622.
Months of mediation by Egypt, Qatar and the United States in indirect negotiations between Israel and Hamas have yet to result in a breakthrough. A diplomatic push to clinch a deal has picked momentum over the past few days.
Late Friday evening, US Secretary of State Antony Blinken said at an event in Arizona that it was challenging to understand Hamas' thought process.
"The leaders of Hamas that we're indirectly engaged with through the Qataris, through the Egyptians, are of course living outside of Gaza, living in Qatar or living in [Turkey], other places, and the ultimate decision-makers are the folks who are actually in Gaza itself with whom none of us have direct contact," he said.
Blinken said if Hamas was really concerned about the well-being of the Palestinians, then agreeing to the ceasefire deal that is on the table should be a "no-brainer."
On Saturday, the Israel Defense Forces (IDF) said it carried out an airstrike on a rocket launch site in the southern Gaza Strip.
Fighter jets hit the militant site near the city of Khan Younis after a rocket was fired from there toward the Ein HaShlosha kibbutz on Friday, the IDF said.
A mortar launching site in central Gaza was also destroyed, a statement said. The Israeli navy has also conducted strikes along Gaza's coast over the past day.
According to Palestinian security services, the Israeli army attacked a building in the village of Abasan in the east of Khan Younis and shelled refugee camps in the central part of the Palestinian territory.
It said at least one Palestinian was killed in the Israeli navy strikes.
(IANS/DPA)
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