CAIRO (Reuters) -Egypt has stepped up diplomatic efforts to enable aid deliveries into Gaza and to de-escalate fighting, the Egyptian presidency said on Sunday, as U.S. Secretary of State Antony Blinken stopped off in Cairo as part of a regional tour.

Aid from several countries has been building up in Egypt's Sinai peninsula due to a failure to reach a deal enabling its safe delivery to Gaza along with evacuations of some foreign passport holders through the Rafah crossing into Egypt.

Israeli bombardments on the Gaza side of the Rafah crossing into Egypt, the main crossing out of Gaza not controlled by Israel, have disrupted operations there.

U.N. aid chief Martin Griffiths said on Saturday that the humanitarian situation in Gaza was becoming untenable.

There is alarm in Egypt over the prospect that residents in Gaza could be displaced by Israel's siege and bombardment, launched in retaliation for the devastating incursion by Hamas militants.

Like other Arab states, it has said that Palestinians should stay on their lands as the war escalates, and that it is working to secure delivery of aid.

A statement from Egyptian President Abdel Fattah al-Sisi's office, issued after a meeting of the national security council, said Egypt rejected any plan to displace Palestinians "to the detriment of other countries" and that Egypt's own security was a red line.

Sisi also proposed a summit to discuss the crisis, according to the statement.

Egyptian Foreign Minister Sameh Shoukry told CNN on Saturday that the Rafah crossing was open but the roads leading to it in Gaza were "inoperable" due to Israeli bombardment. He said that if foreign nationals were able to cross the border Egypt would facilitate their departure to their home countries.

The United States has been part of the diplomatic push to facilitate aid and evacuations through Rafah, and told its citizens in Gaza on Saturday they could move closer to the crossing in case it opened.

Eight planes laden with aid from Turkey, the United Arab Emirates, Jordan, Tunisia, and the World Health Organization have landed in Sinai's Al Arish airport in recent days, according to security sources, and a convoy of more than 100 trucks is waiting in the city awaiting permission to enter Gaza.

(Reporting by Mohamed Waly, Omar Abdel Razek, Yusri Mohamed, Humeyra Pamuk; Writing by Adam Makary, Nafisa Eltahir and Aidan Lewis; Editing by Louise Heavens, Hugh Lawson and Andrew Cawthorne)