Abbas made the demand at a joint news conference with visiting Quartet Committee representative James Wolfensohn in the West Bank city Ramallah.
Wolfensohn, former World Bank chief, was newly appointed as special envoy on behalf of the United States, the United Nations, the European Union and Russia, dubbed the "Quartet Committee", to help coordinate Israel's planned Gaza withdrawal and to spearhead reconstruction there once the Palestinians take over.
"The coming Israeli pullout should be full and comprehensive," said Abbas, while urging Wolfensohn to press Israel to provide the Palestinian side with all the needed information related to the withdrawal.
"Israel should also set up a safe passage linking the Gaza Strip and the West Bank after implementing the evacuation," he added.
Israel currently blocks free movement of people and goods between the two areas.
The Jewish state has proposed to build a railway between Gaza and the West Bank instead of a safe passage after the pullout, a suggestion rejected by Palestinian Minister of Civilian Affairs Mohammed Dahlan who is in charge of Palestinian coordination efforts with Israel.
Reasoning that it would take more than three years for the railway to come into operation, Dahlan accused Israel of not being serious in building a direct and permanent link between Gaza and the West Bank.
Abbas also briefed Wolfensohn on the current situation in the Palestinian lands during their talks, said Dahlan, who also attended the meeting.
Earlier in the day, Wolfensohn met with Palestinian Prime Minister Ahmed Qurei.
Israel is scheduled to pull out troops and settlers from all 21 settlements in the Gaza Strip and four of 120 enclaves in the West Bank from mid August.
To avoid violence during and after the unprecedented withdrawal, Israel has agreed upon coordination with the Palestinians during the evacuation.