Palestinian Authority (PA) Chairman Mahmoud Abbas and Hamas leader Khaled Meshaal issued a joint appeal for an end to "Israeli aggression" in Gaza during talks in Doha on Monday.
Meeting for the first time since the start of Operation Protective Edge on July 8, the two men also called for Israel to lift its blockade of the
They "underlined the necessity of an end to the Israeli aggression and a lifting of the blockade", chief Palestinian negotiator Saeb Erekat said.
He said the two men also "decided to hold further consultations with different Palestinian factions and contacts" on ceasefire efforts.
Azzam al-Ahmed, a senior official in Abbas's Fatah party, is to travel to Egypt, which last week proposed a ceasefire plan supported by the Arab League but rejected by Hamas, Erekat said.
According to Ahmed, "it was decided that there should be a ceasefire first, and we will continue discussions with Egypt and all regional and international sides until we crystallise the content of a final peace agreement."
"Hamas and Abbas agreed that all Palestinian factions should work as a team towards a ceasefire," he told AFP.
UN chief Ban Ki-moon arrived Monday in Cairo, where US Secretary of State John Kerry was also due later the same day, as international efforts to secure a ceasefire gathered pace.
Hamas categorically rejected attempts for a cease-fire in multiple statements, insisting that the terms of the agreement 'did not apply' to them.
The Palestinian Authority has supported these demands.
"These are not conditions but engagements that Israel must honor," Erekat said Monday.
Last week, Abbas encouraged Hamas to accept internationally-brokered ceasefire efforts - if not in the name of Palestinian Arab unity, then at least specifically to hurt Israel.
"Israel accepted the ceasefire proposal. We (the Palestinians) must also accept it so that we can put the Israeli side at unease," Abbas told a news conference with Turkish President Abdullah Gul in Istanbul in comments translated from Arabic into Turkish.