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* German leader urges Egypt dialogue with opposition
* Egyptian president cancels Paris leg of Europe trip
* Seeks badly needed foreign investment
* West unsettled by post-revolution violence
By Edmund Blair and Alexandra Hudson
CAIRO/BERLIN, Jan 30 (Reuters) - German Chancellor Angela Merkel urged Egypt's Islamist president on Wednesday to open a dialogue with all political forces in the crisis-ridden Arab country after a week of violence that has killed more than 50 people.
President Mohamed Mursi flew to Germany to try to convince Europe of his democratic credentials, but in a sign of the political tensions back home, he restricted his trip to a few hours and cancelled a planned Paris leg.
"One thing that is important for us is that the line for dialogue is always open to all political forces in Egypt, that the different political forces can make their contribution, that human rights are adhered to in Egypt and that of course religious freedom can be experienced," Merkel told Mursi at a joint news conference.
The Egyptian leader, who has faced months of protests by liberal and youth groups opposed to a new Islamic constitution, replied that dialogue was possible and that Egypt would be a state based on the rule of law, not run by the military.
But he refused to give a commitment sought by the opposition to form a national unity government, saying that would be for the new parliament to decide after elections expected in April.
Two more protesters were shot dead before dawn near Cairo's central Tahrir Square on the seventh day of what has become the deadliest wave of unrest since Mursi took power in June.
The army chief warned on Tuesday that the state was on the brink of collapse if Mursi's opponents and supporters did not end street battles that have marked the two-year anniversary of the revolt that toppled autocrat Hosni Mubarak.
Mursi is due to return to Cairo later in the day.
Near Tahrir Square on Wednesday morning, dozens of protesters threw stones at police who fired back teargas, although the scuffles were brief.
"Our demand is simply that Mursi goes, and leaves the country alone. He is just like Mubarak and his crowd who are now in prison," said Ahmed Mustafa, 28, a youth who had goggles on his head to protect his eyes from teargas.
Opposition politician Mohamed ElBaradei called for a meeting of the president, ministers, the ruling party and the opposition to halt the violence. But he also restated the opposition's precondition that Mursi first commit to seeking a national unity government.
Mursi's critics accuse him of betraying the spirit of the revolution by keeping too much power in his own hands and those of his Muslim Brotherhood, the Islamist movement banned under Mubarak which won repeated elections since the 2011 uprising.
Mursi's supporters say the protesters want to overthrow Egypt's first democratically elected leader. The unrest has prevented a return to stability ahead of parliamentary elections due within months, and worsened an economic crisis that has seen the pound currency tumble in recent weeks.
The worst violence has been in the Suez Canal city of Port Said, where rage was fuelled by death sentences passed against soccer fans for deadly riots last year. Mursi responded by announcing on Sunday a month-long state of emergency and curfew in Port Said and two other Suez Canal cities.
Protesters have ignored the curfew and returned to the streets. Human Rights Watch called for Mursi to lift the decree.
Mursi was keen to allay the West's fears over the future of the most populous Arab country in his meetings with Merkel and powerful industry groups in Berlin.
"We have seen worrying images in recent days, images of violence and destruction, and I appeal to both sides to engage in dialogue," German Foreign Minister Guido Westerwelle said in a radio interview on Wednesday ahead of Mursi's arrival.
Germany's "offer to help with Egypt's transformation clearly depends on it sticking to democratic reforms", he added.
Germany has praised Mursi's efforts in mediating a ceasefire between Israel and Palestinians in Gaza after a conflict last year, but became concerned at Mursi's efforts to expand his powers and fast-track a constitution last year.
Berlin was also alarmed by video that emerged in recent weeks showing Mursi making vitriolic remarks against Jews and Zionists in 2010 when he was a senior Brotherhood official. Germany's Nazi past and strong support of Israel make it highly sensitive to anti-Semitism.
Mursi's past anti-Jewish remarks were "unacceptable", Westerwelle said. "But at the same time President Mursi has played a very constructive role mediating in the Gaza conflict."
Asked about those remarks at the news conference with Merkel, Mursi said they had been taken out of context and he was not against the Jewish faith.
Egypt's main liberal and secularist bloc, the National Salvation Front, has so far refused talks with Mursi unless he promises a unity government including opposition figures.
"Stopping the violence is the priority, and starting a serious dialogue requires committing to guarantees demanded by the National Salvation Front, at the forefront of which are a national salvation government and a committee to amend the constitution," ElBaradei said on Twitter.
Those calls have also been backed by the hardline Islamist Nour party - rivals of Mursi's Brotherhood. Nour and the Front were due to meet on Wednesday, signalling an unlikely alliance of Mursi's critics from opposite ends of the political spectrum.
Brotherhood leader Mohamed El-Beltagy dismissed the unity government proposal as a ploy for the Front to take power despite having lost elections. On his Facebook page he ridiculed "the leaders of the Salvation Front, who seem to know more about the people's interests than the people themselves".
German industry leaders see potential in Egypt but are concerned about political instability.
"At the moment many firms are waiting on political developments and are cautious on any big investments," said Hans Heinrich Driftmann, head of Germany's Chamber of Industry and Commerce.
Mursi's supporters blame the opposition for preventing an economic recovery by halting efforts to restore stability. The opposition says an inclusive government is needed to bring calm.