And should "recognise, and co-operate with the Special Tribunal for Lebanon", which is a special committee consisting of Lebanese and international jurists, created to try those responsible for the murder of Rafiq al-Hariri, the former prime minister, last year.
EU leaders also condemned the killing of Pierre Gemayel, the outspoken anti-Syrian Lebanese industrial minister, last month and decried any other attempts to "destabilise Lebanon through political assassinations or terrorist acts".
Declaration on Iran
In a special declaration on Iran, the Council expressed concern about "the negative impact of Iranian policies on stability and security in the Middle East".
In trying to determine a solution to the Iranian nuclear issue, the Council stated that it "regrets that Iran has not engaged seriously with the far-reaching proposals presented" to the country and that it "deplores Iran's failure to take the steps required by the IAEA ... and the UN Security Council".
The EU declaration on Iran reflected disillusionment after three years of unproductive talks over nuclear development, which many European nations suspect is aimed at developing atomic weapons.
The council went on to attack Iran over its statements against the EU, the Holocaust, Israel and the continuing deterioration in human rights and political freedoms of its citizens.
Further to the concluding statement from the European summit, Jacques Chirac, the French president, condemned "a destabilisation offensive" against the elected government of Fouad Siniora, the Lebanese premier.
He said: "More than ever, Lebanon needs our help."
The 25 EU nations stood united in their support of "the democratic institutions in Lebanon and, as a result, in support of Siniora's democratically elected government, President Chirac said.
"Our security and our prosperity depend also on the stability in this troubled region.
"We cannot appear divided or inactive as a spiral of uncontrolled violence looms".
Hezbollah, with the support of Syria and Iran, and other pro-Syrian opposition groups, have staged mass demonstrations to try to topple Siniora's Western-backed government.
The EU also urged Israel to stop violations of Lebanese airspace with flights that have created tension with the mainly European UN peacekeeping force in Southern Lebanon.
Deal for Palestinians
Also on Friday, the EU extended an aid deal for the Palestinians by three months, which bypasses the Hamas-led government that took office earlier this year.
Hamas's refusal to recognise Israel has resulted in diplomatic and economic isolation from the international community and triggered a financial crisis for Palestinians.
EU leaders said "the protracted deterioration" of the Palestinian situation justified continuing the World Bank-monitored aid scheme that has funnelled hundreds of millions of euros directly to Palestinians.