Lambrinidis told reporters after the meeting that he discussed with Abbas the "vision of the Palestinians" to acquire an internationally recognised state, as well as the "very delicate" negotiations and discussions currently taking place, both with the Palestinians and the Israelis.
Noting an earlier meeting of the 27 EU foreign ministers, Lambrinidis said "it is a very delicate process which we hope will bear fruit so that there will be real negotiations after whatever takes place at the UN, but not vague negotiations, negotiations aimed at a real solution of the problem and the creation of a Palestinian state that will live peacefully and with security next to an Israeli state".
"We need to finally achieve this," he added.
Asked what Greece's position will be if the Palestinian petition for an independent state is put to the UN General Assembly, Lambrinidis said that "given the discussions taking place right now, it is very important that this effort not only will not be blocked but that it will advance the negotiations process and send a clear and strong message everywhere that Palestine has the right to a state and that Israel has the right to security", adding that "this is what we are discussing at this time".
To a question whether a single position on the issue was formulated during the meeting of the EU foreign ministers, Lambrinidis opined that "there will be no collision of trains", as many sides predict.
The important thing, however, is not so much the European Union having a single position but that Europe will be able, with credibility and dynamism, and united, to advance this process. "Everyone is now looking to us. A few years ago, we were ignored, as Europe, but no we are considered catalysts of the process. And this is what I and many other foreign ministers of the EU are trying to ensure," Lambrinidis said.
The Greek foreign minister's itinerary for Wednesday includes a ministerial conference on Libya and a working lunch of the 27 EU foreign ministers with their Russian counterpart Sergei Lavrov, while he will also address a dinner in his honour hosted by the Foreign Policy Association.
Lambrinidis outlined the various aspects of the economic crisis and the 'immense changes' taking place in Greece, in an interview early Wednesday (Greek time) on the CNBC television network's "The Kudlow Report".
"We are near to an agreement" with the EU-IMF troika, Lambrinidis said, but pointed out three main problems: First, despite the fact that 'dramatic changes' have been made in Greece recently, everything was not done perfectly and satisfactorily. Second, the recession in Greece was bigger than expected. Third, the markets perceived that Europe was not "speaking with one voice".
He also predicted that Greece will be in a tough situation for many years but, despite the negative speculations that appear from time to time, "we are still here, and Europe is still here, and the euro is still a very strong currency", adding his conviction that Greece will avoid default and "absolutely" remain inside the euro zone.
Lambrinidis explained that the planning is already in place, not only for what Greece needs to do now but what it has to do up to 2014.
"Greece is not a poor country. It's a country that was poorly managed for a few years," he said.