At a meeting in Brussels with EU foreign ministers, Abbas repeated his call for east Jerusalem as capital as he urged EU governments to recognize a state of Palestine immediately, arguing that this would not disrupt negotiations with Israel on a peace settlement for the region.
While Abbas made no reference to Trump's move on Jerusalem or US Vice President Mike Pence's visit to the city on Monday, his presence at the EU headquarters in Brussels was seized on by European officials as a chance to restate opposition to Trump's Dec. 6 decision to move the US Embassy to Jerusalem.
Mogherini, in what appeared to be a veiled reference to Trump's recognition of Jerusalem as capital of Israel, called on those involved in the process to speak and act "wisely", with a sense of responsibility.
"I want to reassure President Abbas of the firm commitment of the European Union to the two-state solution with Jerusalem as the shared capital of the two states", Mogherini said.
Before Abbas' arrival, she was more outspoken, saying: "Clearly there is a problem with Jerusalem. That is a very diplomatic euphemism", in reference to Trump's position.
Deputy German Foreign Minister Michael Roth told reporters that Trump's decision had made peace talks harder but said all sides needed to resolve the Israeli-Palestinian conflict.
Abbas also struck a more diplomatic tone than in his recent public remarks, including earlier this month when he said he would only accept a broad, internationally-backed panel to broker any peace talks with Israel.
"We are keen on continuing the way of negotiations", Abbas said. "We are determined to reunite our people and our land".
But his call for the European Union to immediately and officially recognize a state of Palestine was unlikely to be answered, two senior EU diplomats said.
While nine EU governments including Sweden and Poland already recognize Palestine, the 28-nation bloc says such recognition must come as part of a peace settlement.
Only Slovenia has recently raised the possibility of recognizing the state of Palestine. A parliamentary committee there is due to consider the issue on Jan. 31, but it remains unclear when the parliament could recognize Palestine.
That reflects the European Union's dual role as the Palestinians' biggest aid donor and Israel's biggest trade partner, even if EU governments reject Israeli settlements on land Israel has occupied since a 1967 war - including the West Bank, east Jerusalem and the Golan Heights.
The European Union also wants the Palestinians to remain open to a US-led peace plan, expected to be presented soon by Jason Greenblatt, Trump's Middle East envoy and Trump's son-in-law and senior adviser, Jared Kushner.
Abbas said there was "no contradiction between recognition (of Palestine) and the resumption of (peace) negotiations".
Instead, France wants to push the European Union to offer closer trade ties through a so-called EU association agreement, an EU treaty covering unfettered access to the bloc's 500 million consumers, aid and closer political and cultural ties.
"We want to say to Mahmoud Abbas that we want to move ... towards an association agreement and to start the process already", said France's Foreign Minister Jean-Yves Le Drian.
But offering an EU association agreement to the Palestinians was also fraught with difficulties, diplomats said.
Under EU rules, the agreements need to be agreed with sovereign states. France argues that the EU has an association agreement with Kosovo, whose independence is not recognized by all countries, including EU member Spain.