In a speech to the Parliament's plenary in Brussels on Thursday, Abbas launched a blistering attack on Israel, accusing it of pursuing a "colonisation" policy and "building walls."
He said, "No country should be allowed to wipe another country off the map. All we want to do is exist."
His comments come a day after Israel's President Reuven Rivlin, also speaking in Parliament, warned that there was no prospect of a peace deal with the Palestinians in the near future and urged the EU to show patience and put its weight behind measures to facilitate future negotiations.
Rivlin criticised France's peace-conference initiative, launched earlier this month, which he said amounted to "negotiations for negotiations' sake" and would only deepen divisions between Israelis and Palestinians.
Rivlin said any peace deal was impossible for now, because of divisions between the Palestinian Authority and Hamas, which rules in the Gaza Strip, as well as regional turmoil and the absence of economic conditions to build confidence between the two sides.
He drew parallels between the gradual process of European peace-building and the current deadlock in Israeli-Palestinian negotiations.
Abbas, in his address, called the French peace push a "vital conference for our region and the whole world."
He told deputies Palestinians had suffered a "series of historic massacres" and a "sort of occupation not seen in the 20th and 21st centuries."
"We are still living through a black period, with arbitrary action by Israel and hateful racism. In terms of finding a peaceful solution we are not making any progress with Israel."
Addressing a formal sitting of Parliament, he said one million Palestinians had been jailed by Israel and 7000 of his compatriots were currently held by Israel as prisoners of war.
Abbas was sat alongside European Parliament President Martin Schulz, who emphasised the "importance" the assembly placed on its relations, including economic cooperation, with the Palestinian Authority.
The German Socialist MEP said he believed the presence of both Abbas and Rivlin in Brussels this week sent a signal that efforts to find a peaceful solution to the conflict between the two sides "is still alive."
He respected Israel's "right to live in safety" but also stressed the importance of a "free and peaceful" Palestine.
His intervention comes with EU officials saying on Thursday that they were still hoping that Abbas and Rivlin would meet and talk during their visit to Brussels.
That would be the highest level meeting between the Israeli and Palestinian leadership since talks in 2014.
No meeting had taken place by Wednesday evening, though Israeli officials said Rivlin was ready to meet Abbas "anytime, anywhere."