Israel has secured US and European pledges to help to prevent Hamas, which it says receives weapons from Iran, from rearming through tunnels under the Gaza-Egypt border and by sea. Egypt has also limited movement through its Rafah crossing with the Gaza Strip.

But the tunnels have been the only way for Gazans to get the commercial goods that Israel keeps out, and they have already begun to rebuild the ones that Israeli bombs destroyed. Ismail Haniyeh, Hamas’s leader in the Gaza Strip, said a ceasefire deal “must guarantee the lifting of the siege”.

Under a 2005 agreement brokered by the United States, the Authority was to help to oversee border crossings. The deal gives Hamas no role.

Israeli Prime Minister Ehud Olmert told Mitchell on Wednesday that Israel would not reopen any Gaza crossings, except for aid shipments, until an Israeli soldier captured in 2006 was freed, an Israeli official said.