BRUSSELS, June 15 (Reuters) - The European Union joined Washington on Friday in declaring its support for Mahmoud Abbas as the legitimate leader of the Palestinians after the Islamist movement Hamas seized control of the Gaza Strip. Russia called for calm and urged international mediators to help to avert civil war, while Egypt pulled its diplomats out of Gaza in protest at the Hamas takeover and Iran said the violence showed Palestinians had lost sight of their true enemy. Foreign ministers of the Quartet of international peace mediators -- the United States, the European Union, Russia and the United Nations -- were due to hold a telephone conference on Friday to discuss the situation, a spokeswoman for the European Commission said. "We fully support President Abbas," she added. "We call on President Abbas, the legitimate president of all Palestinians, to (do) his utmost to resolve the situation through dialogue and to work towards national unity and reconciliation." The EU position mirrored that of Washington, which on Thursday endorsed Abbas's decision to declare a state of emergency and vowed to stand behind Palestinian moderates. "We fully support him in his (effort) to try and end this crisis for the Palestinian people," Secretary of State Condoleezza Rice told reporters in Washington. Hamas, an Islamist group that won a parliamentary election last year, is considered a terrorist organisation by the United States, the European Union and Israel. The United States has led efforts to isolate the Hamas-dominated government, demanding that it renounce violence, recognise Israel's right to exist and abide by existing agreements with the Jewish state. RUSSIA CONCERNED Russian President Vladimir Putin spoke with Israeli President Shimon Peres about the situation, which the Kremlin said caused "serious concern". "The bloodshed is continuing and it is important to help the Palestinians to reunite. Civil war in Palestine is in no one's interest," Foreign Minister Sergei Lavrov told reporters. British Foreign Secretary Margaret Beckett said: "Once again, extremists carrying guns have prevented progress against the wishes of the majority who seek a peaceful two-state solution ... "It is imperative that all sides agree to speak to each other. Dialogue is the only way to achieve a long lasting and sustainable peace," she added. The head of Egypt's diplomatic mission in Gaza, Major-General Burhan Hammad, left with his entire staff as Hamas declared it had seized control of Gaza. "Of course it was a protest measure," said one official familiar with the decision, who declined to be identified. The Egyptian walkout is a blow to Hamas, which has long been welcomed in Cairo despite being shunned by Western powers. The official said it would now "take some time" to decide how relations would now be handled. Iran, a key ally of Hamas, also signalled its displeasure with the upheaval. "Unfortunately, Palestinian fighters have forgotten their main enemy and are fighting against each other instead of the Zionist regime (Israel)," said former president Akbar Hashemi Rafsanjani, he told worshippers at Friday prayers in Tehran. "This ... is in line with the enemy's interests. It's exactly what they want."