Abbas' visit comes amid an international backlash against Israel after its forces boarded a Turkish aid ship headed for the Hamas-ruled Gaza Strip on May 31. Nine pro-Palestinian activists of Turkish origin were killed.
"We cannot announce from our side the independent Palestinian state, because we are committed to the agreements that we have made with Israel, and these agreements state that one party does not have right to do anything that is one-sided, that could effect the final results," Abbas said.
He said that he was "satisfied with the EU's role and political position" on Gaza.
The EU has been working with the Palestinian Authority to build up the institutions of a future democratic, independent and viable Palestinian state living side by side with Israel and its neighbours.
These efforts are regularly debated by the EU Council of Ministers.
The EU is the biggest supplier of aid to the Palestinian territories, with member states and the executive European Commission providing about $720 million a year.
The European Union is pushing to free up trade with the territories.
Israel imposed the blockade when Hamas seized control of Gaza from Abbas' Fatah-dominated Palestinian Authority in 2007 after winning parliamentary elections.
Israel says the siege is designed to prevent arms being smuggled to Hamas and other armed groups.
Abbas now governs only the West Bank.