The mediation talks were led by Egypt, Qatar and Turkey, and have had support from Saudi Arabia and the US, a Palestinian source told Xinhua news agency on Wednesday.
The source, who requests anonymity, said that the regional move aimed to provide safe passage with the possibility of declaring a humanitarian truce in the Gaza Strip and its surroundings in order to evacuate foreigners through the Rafah crossing, the sole crossing point between Egypt and the Palestinian enclave.
Egypt, the Palestinian Authority, and other regional countries are pressing for the entry of humanitarian aid, including fuel, into the Gaza Strip to avoid a severe humanitarian disaster threatening its population, said the source.
According to the source, Hamas and the Palestinian factions agreed to the mediation, while the American administration and Arab countries are pressuring Israel to accept this in order to proceed with its implementation as soon as possible.
Hamas on Saturday launched a surprise attack on Israeli towns adjacent to the Gaza Strip, prompting Israel to launch retaliatory strikes on Gaza.
As of Wednesday, more than 2,000 people have been killed and thousands more injured on both sides.
After the Hamas attack, Israel cut off its power supply to the Gaza Strip and ordered a complete siege on the Palestinian enclave.