* Ceasefire holds into a third day
* Egyptian mediators continue shuttle diplomacy
* U.N. to launch aid appeal for Gaza (Adds U.S., UAE comments; Egypt-Jordan meeting)
JERUSALEM/GAZA, May 23 (Reuters) - A ceasefire between Israel and Hamas held into a third day on Sunday as mediators spoke to all sides about extending the period of calm after the worst outbreak of fighting in years.
Egyptian mediators have been shuttling between Israel and the Gaza Strip, which is ruled by Hamas, to try to sustain the ceasefire and have also met the Islamist group's rival, Palestinian President Mahmoud Abbas, in the occupied West Bank.
Egypt's foreign minister was also set to meet with top Jordanian officials on Sunday to discuss de-escalation and ways to revive the Middle East peace process.
Lynn Hastings, the United Nations Humanitarian Coordinator for the Palestinian territories, said on Sunday the U.N. would launch an appeal to repair the damage in densely populated Gaza, where there is a threat of COVID-19 spreading.
"The escalation has exacerbated an already dire humanitarian situation in Gaza, generated by nearly 14 years of blockade and internal political divisions, alongside recurrent hostilities," she said in a statement issued from the Palestinian enclave.
"We must also ensure support to continue addressing needs that already existed, including those arising from the ongoing pandemic."
Israel has blockaded Gaza since 2007, saying this prevents Hamas bringing in arms. Hastings said the United Nations had long been asking Israel to stop the blockade and would continue doing so.
U.S. President Joe Biden has said Washington will work with U.N. agencies on expediting humanitarian aid for Gaza "in a manner that does not permit Hamas to simply restock its military arsenal".
His top diplomat, U.S. Secretary of State Antony Blinken, in television interviews on Sunday said that while the Biden administration was now focused was on aid, reconstruction and diplomacy, an end to violence could help shift gears toward long-term peace.
"We'll be re-engaging with the Palestinians -- of course continuing our deep engagement with the Israelis -- in trying to put in place conditions that allow us over time, hopefully, to advance a genuine peace process. But that is not the immediate order of business," Blinken told CNN's "Fareed Zakaria GPS" program. "We have a lot of work to get to that point."
The United Arab Emirates on Sunday also said it stands ready to facilitate peace efforts.