The Israeli military said one rocket was launched at the Tel Aviv area, in Israel's commercial heartland, before the ceasefire began on Sunday night and may have landed in the sea. Gaza's dominant Hamas group said it fired the missile.
Hamas is demanding an end to Israeli and Egyptian blockades of the Gaza Strip and the opening of a seaport in the enclave - a project Israel says should be dealt with only in any future talks on a permanent peace deal with the Palestinians.
A month of war has killed 1,938 Palestinians and 67 Israelis while devastating wide tracts of densely populated Gaza, and Egypt's Foreign Ministry has urged both sides to work towards "a comprehensive and lasting ceasefire agreement".
Hamas spokesman Sami Abu Zuhri said the new negotiations would be "the last chance" for an agreement. Israeli representatives are not meeting face-to-face with the Palestinian delegation because it includes Hamas, which Israel regards as a terrorist organisation.
Israeli Strategic Affairs Minister Yuval Steinitz said disarming Gaza militants was crucial to sustain a long-term truce and he hoped this could be done by diplomacy rather than force.
He said: "I certainly hope there will be a diplomatic solution. If there will not be a diplomatic solution, I am convinced that sooner or later we will have to opt for a military solution of taking temporary control of Gaza to demilitarise it again."
Another sticking points in the Cairo talks has been Israel's demand for guarantees that Hamas would not use any reconstruction supplies sent to Gaza to build tunnels of the sort Palestinian fighters have used to infiltrate Israel.
Hamas has demanded an end to the economically stifling blockade of the enclave imposed by both Israel and Egypt, which also sees the Islamist movement as a security threat.
Israel has resisted easing access to Gaza, suspecting Hamas could then restock with weapons from abroad.
According to the UN, at least 425,000 displaced people in the Gaza Strip are in emergency shelters or staying with relatives. Nearly 12,000 homes have been destroyed or severely damaged by Israeli attacks.
In Gaza yesterday, shops began to open and traffic was normal as some displaced families returned to the homes they had been forced to abandon during Israeli attacks, expressing hopes this truce would last after a series of failed ceasefires.
The new three-day ceasefire won praise from UN Secretary General Ban Ki-moon, who said he hoped it would lead to a durable ceasefire.
Israeli air strikes and shelling on Sunday killed nine Palestinians in Gaza in a third day of renewed fighting since the last truce ended.
One air strike destroyed the home of Gaza City's mayor Nezar Hijazi. There were no casualties in the attack because Israel telephoned warnings to residents in the house and neighbouring buildings.
Meanwhile, a Turkish aid group has said it will send ships again to challenge the Israeli blockade of Gaza, four years after Israeli commandos stormed its flotilla.