It remains the only direct opening to the rest of the Arab world from territory that Israel handed to the Palestinians two months ago, and the failure to negotiate its permanent opening has become a symbol of Gaza's isolation.
Seeking to nudge the two sides forward, Rice met separately today with Israeli Prime Minister Ariel Sharon and Palestinian Authority President Mahmoud Abbas.
In a sign of the Bush administration's desire for a breakthrough on the border issue, Rice put off plans late today to fly to Asia after a brief stop in Jordan. Instead, she said she would return to Jerusalem in hopes of brokering a deal.
"We're still working the issues with both sides," Rice's spokesman, Sean McCormack, said today as the secretary left for Amman, the scene of hotel bombings last week that killed 57 people.
Abbas said after his visit with Rice that the two sides had all but reached agreement. Later today, Israeli officials said a deal appeared near as talks continued.
"With some will, and with some creativity, agreement ... should be within sight," Rice told a news conference. "I'm never going to predict precisely when this is going to come to a conclusion, but I do think they have made a lot of progress."
Rice said envoy James Wolfensohn, who has mediated talks on border crossings and other economic issues since the Israeli pullout, had put forward new U.S. proposals to bridge differences between the two sides. Rice met for an hour today with Israeli Prime Minister Ariel Sharon.
Abbas said the two sides appeared close to an agreement and Israeli officials echoed that today as talks continued.
The difficulties in working out a solution for Rafah underscored the difficulties of resolving even comparatively minor points on the path to the much larger goal of negotiating peace and establishing an independent Palestine state. Although many had hoped the Gaza withdrawal would inject new momentum into the peace process, little progress has been made toward that vision since.
As with so many aspects of relations between the Israelis and Palestinians, the biggest barrier to resolving the border crossing issue appears to be mutual mistrust.
Immediately after Israel pulled its last soldiers from a patrol zone along Gaza's southern border in August, Palestinian and Egyptian security guards at Rafah were overwhelmed as thousands of residents, heady with their new freedom, rushed into Egypt to visit relatives they had not seen in years or to buy goods at cut-rate prices.
The episode unnerved Israeli authorities, who have not allowed the Rafah crossing to open since then. The port was the primary means for Gaza's 1.3 million residents to leave the impoverished coastal strip.
Rice hoped to close the remaining distance between Israel's need for assurances of tight border controls and the Palestinians' desire to protect their sovereignty and ensure that ordinary residents could move in and out freely.
The two sides came closer with a recent compromise that envisions the presence of European Union monitors to keep watch over crossings at Rafah. But differences remain over how much control the monitors would be able to exercise and the extent of Israel's role in overseeing border movement, even indirectly through maintaining a database of crossers or via surveillance cameras.
"We need to augment the Palestinian [security] weakness without insulting the Palestinians," an Israeli government official, who declined to be identified because of the subject's sensitivity. "We know they will stop somebody carrying [weapons], but if someone big in a militant group walks across with $50,000 in a satchel, that's five suicide bombers."