"We have a meeting tonight to discuss the ways EU can contribute to a de-escalation," Mogherini said in brief comments before a working dinner.
The EU`s diplomatic chief said she hoped the pair would discuss "concrete steps on the ground, including difficult ones, that can strengthen the Palestinians on an everyday basis".
The European Commission is the biggest provider of financial aid to the Palestinians, providing more than 5.6 billion euros ($6.19 billion) to Abbas` Palestinian Authority since 1994.
Mogherini, who met with Israeli Prime Minister Benjamin Netanyahu in Berlin on Thursday, admitted there was "a certain degree of frustration" in Europe over the peace process, which collapsed in April 2014 amid bitter recriminations.
Abbas repeated his criticism of what he said was Israel`s "non-respect" for the rules at Jerusalem`s Al-Aqsa mosque compound, sacred to both Muslims and Jews, which is at the centre of the recent wave of violence.
"The situation in Palestine is extremely serious and grave and may even deteriorate. This is my fear," he said.
"The main reason is the feeling of disappointment (among) the young generation," who feel there is "no hope," Abbas said.
Palestinians accuse Israel of seeking to change the rules that allow Jews to visit, but not to pray there. Israel denies it has violated the status quo.
Stabbings and violent protests have become daily occurrences since simmering tensions over the compound boiled over in early October, leaving scores dead.
Abbas urged a revival of peace negotiations, calling for Israel to halt settlement-building in the West Bank and prevent "incursions" on the al-Aqsa compound.
Mahmud Abbas at EU to siscuss surging Israel-Palestinian violence
27 October 2015
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The European Union`s foreign policy chief Federica Mogherini met Palestinian president Mahmud Abbas late Monday to discuss "concrete steps" to calm the surge of violence between Israelis and Palestinians.
