Palestinian President Mahmoud Abbas, who reached an agreement with Hamas in April that led to the formation of a unity government last month, called for acceptance of the proposal, the official Palestinian news agency WAFA said.
Abbas was due in Cairo on Wednesday for talks with President Abdel Fattah al-Sisi, the Palestinian leader's spokesman said.
The Arab League, at a meeting on Monday, also welcomed the ceasefire plan.
ISRAELI GROUND ASSAULT POSSIBLE
Israel had mobilized tens of thousands of troops for a threatened Gaza invasion if the rocket volleys persisted.
"We still have the possibility of going in, under cabinet authority, and putting an end to (the rockets)," Amos Gilad, a senior Israeli defense official, said.
Under the proposal announced by Egypt's Foreign Ministry, high-level delegations from Israel and the Palestinian factions would hold separate talks in Cairo within 48 hours to consolidate the ceasefire with "confidence-building measures".
Hamas leaders have said any deal must include an end to Israel's blockade of Gaza and a recommitment to a truce reached in an eight-day war there in 2012.
Hamas also wants Egypt to ease curbs at its Rafah crossing with Gaza imposed after the military ousted President Mohamed Mursi, an Islamist, a year ago.
The Egyptian proposal made no mention of Rafah or when restrictions might be eased.
Hamas has faced a cash crisis and Gaza's economic hardship has deepened as a result of Egypt's destruction of cross-border smuggling tunnels. Egyptian authorities also accuse Hamas of assisting anti-government Islamist militants in Egypt's Sinai peninsula, an allegation the Palestinian group denies.
Hamas has said it also wants the release of hundreds of its activists arrested in the West Bank while Israel searched for the three missing teenagers.
The proposed truce also made no mention of the detainees.
Adnan Abu Amer, a political analyst in Gaza, said it appeared that Egypt had deliberately ensured that their initiative would fall short of Hamas's demands, in an attempt bid to make the movement look rejectionist.
"Egypt stood by Israel's side, as if it was trying to punish Hamas and give Israel some time to pursue its military campaign," he said.