Abbas made the appeal in talks with James Wolfensohn, the Middle East quartet's special envoy for Israel's disengagement project on Wednesday.
Abbas said Israel should let the airport and the route for safe passage reopen after withdrawing from the occupied Gaza Strip this summer, Palestinian Civil Affairs Minister Mohammed Dahlan, who was present as the meeting, said in the West Bank city of Ram Allah.
"The president stressed the need for the Israeli withdrawal to be complete and for Israel to supply us with details," Dahlan added.
Open and shut
The international airport in southern Gaza, near the town of Rafah on the Egyptian border, was opened in 1998 and closed by Israel in 2001 following the outbreak of the Palestinian uprising.
Wolfensohn is on a five-day visit
to the region
The "safe passage" linking Gaza to the occupied West Bank was also opened under great pomp and ceremony in October 1999, only to be closed within months, similarly for security reasons.
It had allowed Palestinian people and goods free movement between the two territories.
Appointed envoy by US President George Bush after stepping down as head of the World Bank, Wolfensohn is paying a five-day visit to the region barely two months before Israel is scheduled to start implementing its planned pullout from Gaza.
Meanwhile, Israeli forces on Wednesday imposed a curfew on the village of Marada south of the West Bank city of Nablus.
Residents said Israeli forces wanted to prevent them from staging demonstrations against the building of the separation barrier on the village's lands.
Witnesses said three foreign supporters were arrested and prevented from reaching the village.
In another development, eight members of the Palestinian Legislative Council (PLC) on Wednesday boycotted a session to question the interior and finance ministers.
Aljazeera's correspondent in Ram Allah, Shirin Abu Aqla, quoted deputy head of the PLC Hasan Khraisha as saying that the members staged a sit-in outside the headquarters of the PLC and did not attend the session.
"The president stressed the need for the Israeli withdrawal to be complete and for Israel to supply us with details"
Mohammed Dahlan, Civil Affairs Minister, Palestinian Authority
The members were protesting the postponement of the Palestinian legislative elections due to be held next month.
Meanwhile, to discuss the postponement issue with representatives of a few Palestinian groups, Abbas will arrive in Gaza on Wednesday evening.