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"History has demonstrated that democracies are more stable, viable and prosperous than any alternative," he told a news conference. "With stability comes tourism and investment, and with both come jobs." He said Egypt was a "vital" US partner, on his first stop of a regional tour.
Mr Kerry's visit to Cairo was not disclosed by US officials until he landed. It is the first time a US secretary of state has travelled to Egypt on a visit that is unannounced for security reasons.
The BBC's Kim Ghattas, travelling with Mr Kerry, says it is the kind of precaution that characterises trips by US officials to countries like Afghanistan and Iraq. This is a sign of US concerns about continued instability in the country, but it is also a reaction to the high level of anti-American feeling in Egypt, our correspondent says.
On his six-hour stop Mr Kerry is meeting the interim leaders that assumed control following Mr Morsi's removal in July - President Adly Mahmud Mansour, Prime Minister Hazem el-Beblawi, Foreign Minister Nabil Fahmy and army chief Gen Abdel Fattah al-Sisi.
It is the first stage of a nine-day tour that will take in Middle Eastern and North African countries, as well as Poland. Continue reading the main story Morsi trial Former President Morsi faces charges of inciting the killing of protesters outside the presidential palace in December 2012 14 other senior figures from the Muslim Brotherhood are being tried with him Morsi supporters say his overthrow and detention are illegal and have threatened large street protests With Mr Morsi in court, Egypt will have two former presidents on trial simultaneously, as Hosni Mubarak is being retried Morsi on trial:
Q&A 'Difficult time' Tensions remain high in Egypt, where former President Morsi goes on trial on Monday. His supporters say he was removed in a coup and is now facing a politicised trial. Human rights groups accuse the security services of acting without accountability.
Mr Kerry said he had held "constructive, detailed and frank" discussions with his Egyptian counterpart, Mr Fahmy, and said it was "no secret" that Egypt was going through a "difficult time". "All acts of terror in Egypt must come to an end - all acts," he said - against churches, worshippers, against security services both in the Sinai and elsewhere.
Mr Kerry said Egypt's fortunes, and its bilateral relations, depended on its democratic transition. "The United States believes that the US-Egypt partnership is going to be stronger when Egypt is represented by an inclusive, democratically elected civilian government based on rule of law, fundamental freedoms and an open and competitive economy," he said.
Mr Fahmy said Kerry's comments and the "roadmap" Gen Sisi laid out following the military coup - which sets out constitutional reform and elections by spring 2014 - indicate that "we are all pursuing a resumption of normal relations".
Mr Kerry is also reported to be meeting, behind closed doors, members of Egyptian civil society alarmed by a crackdown in which hundreds of people have died. Last month the US froze a large portion of the $1.3bn (£810m) in aid it sends to Egypt, prompting condemnation from Cairo.
On Sunday, Mr Kerry insisted that was merely a "reflection of US law" and said assistance that went directly to the Egyptian people had been maintained. Relations have been tense since the overthrow of President Morsi, an Islamist, and a subsequent crackdown by new authorities on protests. Hundreds of people have died.
On Saturday, Egyptian newspaper al-Watan published what it said were the first images of Mr Morsi in detention. The images, which have not been independently verified and are undated, show Mr Morsi dressed in a tracksuit and sitting in an armchair, appearing animated and comfortable.
Trade and defence Saudi Arabia, Israel, Jordan and Morocco are among the countries on the next stages of Mr Kerry's itinerary. After his Egyptian visit, Secretary Kerry will go on to the Saudi capital, Riyadh. The Saudi government has recently expressed its disappointment with what it sees as America's hesitant approach in Syria and a lack of support for the new Egyptian government. #
Mr Kerry is expected to discuss defence and trade issues with officials, with Syria likely to be high on the agenda across the region. The secretary of state will also meet Israeli and Palestinian leaders to discuss the peace process in Jerusalem and Bethlehem.
He will then travel to Algeria and Morocco. Correspondents say Mr Kerry may have to face difficult questions over allegations of widespread US spying. In the wake of revelations sparked by leaks from ex-US intelligence contractor Edward Snowden, Mr Kerry said last week that spying by the US National Security Agency may have gone too far.