The move, which includes suspension of the Red Cross programme for families to visit Palestinian prisoners in Israeli jails, follows the kidnap of three UN workers, including a Briton, in Khan Yunis on Monday.
Armed Palestinian militants abducted one Palestinian and two foreign UN Relief and Works Agency (UNRWA) staff after dozens of bullets were fired at the Red Cross office in Khan Yunis.
Witnesses said the three were in a blue-flagged UN vehicle when they were intercepted by Palestinian gunmen. The UNRWA workers Christine Blunt, from the UK, Steven Karl from Switzerland and the Palestinian, Rasmi Balousha, were rescued after Palestinian security forces stormed the house where they were being held shortly after the kidnap. Two bystanders were injured as Fatah militants exchanged gunfire with the security forces, but the UNRWA workers were unhurt.
The abduction, the latest in a series mainly targeting foreigners, was widely attributed in Gaza to supporters of Farouk Kaddoumi, the secretary general of the PLO, and an internal opponent of the Palestinian President, Mahmoud Abbas. Mr Kaddoumi, who lives in Tunis, has set up an office in Gaza with the declared intention of establishing a militia. Palestinian security forces had arrested Suleiman al-Fara, a director of Mr Kaddoumi's office in Khan Yunis and a commander of the Fatah-linked al-Aqsa Martyrs' Brigades.
Yesterday, President Abbas used a special meeting of the Palestinian Legislative Council in Gaza to urge the factions to keep calm during the evacuation of 8,500 Jewish settlers which starts next week. "It is a requirement to ensure the withdrawal will take place in a civilised manner so we can show the world we deserve our freedom and independence," he said on Palestinian television. Mr Abbas also promised that parliamentary elections postponed from July would now be in January.
Juan Coderque, of the ICRC in Gaza, said although field operations had been suspended, staff in the agency's Gaza City office were still working as normal, for example on arranging co-ordination with Israel for Palestinians requiring urgent medical treatment.
He said the Khan Yunis office had been closed for "the time being" pending "intensive" talks with the PA to "clarify" the security situation. Mr Coderque said he did not think the ICRC was being targeted as such and that it had widespread support in Gaza.
Gina Bevevento, a spokeswoman for UNRWA, said the agency was "continuing to deliver services to refugees" but would be "assessing" the security situation. Red Cross officials are seeking security guarantees in talks with the Palestinian Authority.
In June alone, the ICRC enabled 21,000 Palestinians to visit family members in Israeli jails.Reuse content