Abbas, who came to Brussels in search of European support amid a bitter row with Washington over US President Donald Trump's decision to recognise Jerusalem as the Israeli capital, said the Palestinians were still committed to the stalled peace process.
The visit, part of a wider tour of Middle Eastern countries, comes amid simmering Palestinian anger at US President Donald Trump's December recognition of Jerusalem (al-Quds) as the capital of Israel.
"If there were any hopes for a breakthrough on a peace deal, I'd say that's pretty remote after the Jerusalem decision", said Makovsky, a member of the Obama administration's peace negotiations team.
Palestinian chief negotiator Saeb Erekat said on Twitter that Pence's speech showed the USA administration was part of the problem rather than the solution. Mike Pence arrived in Israel on Sunday evening for a three-day visit, the third stop in his delayed trip to the Middle East.
"We truly consider the European Union as a true partner and friend - and therefore we call on its member states to swiftly recognize the state of Palestine", Abbas said ahead of a meeting with EU foreign ministers in Brussels.
The status of Jerusalem has always been a sticking point in peace negotiations between Israelis and Palestinians.
Israeli Prime Minister Benjamin Netanyahu thanked Pence for standing up for the "truth" and supporting Israel at the United Nations. The decision, which is looked as a diversion from the two state policy, has triggered a series of protests by Palestinians across the world.
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The administration previously said that it would take a couple of years at least to find a site for a new embassy in Jerusalem, obtain the proper paperwork, build and secure the facility, and move staff.
The Palestinians have angrily protested against the United States decision to recognise Jerusalem as Israel's capital and say the U.S. can not be trusted as a mediator.
"Obstacles occur here and there, but this will not make us relinquish our belief that the only path for peace is negotiations with global participation and supervision", Abbas said.
Outraged at Trump's Jerusalem declaration, a move that reversed decades of United States policy on the city's status, the Palestinians are snubbing Pence.
Hanan Ashrawi, member of the Palestine Liberation Organization's (PLO) Executive Committee, Monday slammed as "ludicrous" statements by US Vice President Mike Pence that his current Middle East visit was meant to help efforts to broker peace between Israelis and Palestinians.
The Vice-President said he was hopeful "we are at the dawn of a new era of renewed discussions to achieve a peaceful resolution to a decades-long conflict".
In recognising Jerusalem as Israel's capital, Mr Trump has endorsed the Israeli position.