Egypt's intelligence chief met Palestinian leaders and militant factions on Monday at the start of a mission to ensure Palestinians in Gaza can cross its borders more freely after Israeli troops quit the territory.
Greater freedom of movement for Gaza's 1.4 million inhabitants is widely seen as key to boosting the economy of the impoverished coastal strip and bolstering public support for moderate President Mahmoud Abbas and peace moves with Israel.
Palestinian officials said following his talks with Abbas and representatives of 13 armed factions, Egypt's Omar Suleiman would pursue a deal with Israel over the Rafah border crossing between Gaza and Egypt.
Suleiman, visiting Gaza a day after a Palestinian suicide bomber critically wounded two guards at a bus station in southern Israel, made no comment to reporters.
Rafah is under tight Israeli security control and its handover to the Palestinian Authority or a third party could open the gates for many Gazans to leave the territory for the first time in years of conflict with the Jewish state, reports Reuters.
According to Financial Times, the militant groups agreed earlier this year to respect a period of calm in their conflict with Israel, they reserved a right to retaliate for what they regard as Israeli aggression.
The rush-hour blast in Beersheba came shortly after Mr Abbas told Israel Radio that he regarded a ceasefire he declared with Ariel Sharon, Israeli prime minister, in February as indefinite.
Militant groups such as Hamas, the main political opposition to Mr Abbas, insist the term of the period of calm expires at the end of this year.