“The persistent violence in the Arab world fills me with fear. I strongly condemn the attacks against the German embassy in Khartoum, as well as those against several American embassies," Merkel said in a statement.
"Violence must never be the means of political debate. Religious fanaticism must not take the upper hand. Germany calls for a mutual respect of all religions and a dialogue between faiths," she added.
“I call upon all parties in this difficult situation to show calm and think carefully. Arab governments must do everything to ensure security at diplomatic missions," she said.
German Foreign Minister Guido Westerwelle earlier demanded that Khartoum ensure the safety of the German mission.
"I condemn the anti-Islamic hate video but still this cannot be a justification for the outbreak of violence," Westerwelle told reporters. "This violence must stop immediately."
He expressed relief that no German staff were injured when around 5,000 protesters protesting at an anti-Islam film stormed the embassy, leaving it torched and badly damaged.
Two protesters were killed during the riot after it later spread to the US embassy.
Westerwelle later spoke to his Sudanese counterpart Ali Karti by telephone and demanded "a quick and comprehensive safeguarding of the German embassy in Khartoum," a ministry spokesman said.
Karti "assured us that his government will do everything to ensure security," the spokesman said.
“I understand the outrage in the Islamic world," Westerwelle said of the amateurish US-made film, which portrays followers of the Islamic faith as immoral and gratuitously violent.
Westerwelle insisted however that the mob that had stormed the diplomatic missions in Khartoum did not represent "the majority of citizens."
He had announced earlier that Germany had stepped up security at its embassies and consulates throughout the Muslim world in the wake of the violent protests touched off by the video.
He said the Sudanese ambassador to Germany had been summoned to his ministry earlier on Friday and "unequivocally reminded of his government's duty to protect diplomatic missions."
It was not immediately clear why the German embassy came under attack, although Islamists frequently deplore the country's military role in Afghanistan.