WASHINGTON --President Barack Obama on Tuesday challenged Egypt's embattled autocratic ruler, a staunch U.S. ally, to immediately begin the process of transitioning the country to new leadership, a signal that there should be no drawn-out goodbye. Earlier, Egyptian President Hosni Mubarak had announced he would not seek another term in office but also would not yield to growing demands to step down now. After a huddle at the White House, Obama went on television to respond. In his brief statement at the White House, Obama invoked Egypt's ancient and storied past in what appeared to be an appeal to Mubarak's desire to be remembered well in history as a powerful leader and peacemaker. He said he had spoken to Mubarak to press his case for 30 minutes shortly after Mubarak addressed the Egyptian people. "He recognizes that the status quo is not sustainable and that a change must take place," Obama said of Mubarak. "Indeed, all of us who are privileged to serve in position of political power do so at the will of our people." "Through thousands of years, Egypt has known many moments of transformation; the voices of the Egyptian people tell us that this is one of the moments, this is one of those times," Obama said. He added that the United States heard those voices demanding change as anti-government protests filled the streets of Cairo and other Egyptian cities. Mubarak delivered his speech after hearing from a special envoy, former U.S. ambassador to Egypt Frank Wisner, whom Obama dispatched to Cairo on Monday. Wisner's message: The U.S. saw his tenure at an end, didn't want him to stand for re-election in September and wanted him to prepare an orderly transition to real democracy. "It is my belief that an orderly transition must be meaningful, it must be peaceful and it must begin now," Obama said he had told Mubarak in the phone call. That suggested Mubarak's concession was not enough, but Obama left the point dangling. He was careful not to say that Mubarak should have left immediately, and he stressed that it was not up to the United States to pick Egypt's leaders. "Furthermore, the process must include a broad spectrum of Egyptian voices and opposition parties," he said. "It should lead to elections that are free and fair. And, it should result in a government that is not only grounded in democratic principles but is also responsive to the aspirations of the Egyptian people." Obama praised the "passion and dignity" of the protesters who have rallied for Mubarak's departure as an "inspiration" to people around the world, and he hailed the Egyptian military for its poise in handling the situation. "To the people of Egypt, particularly the young people of Egypt, I want to be clear: We hear your voices," Obama said. "I have an unyielding belief that you will determine your own destiny and seize the promise of a better future for your children and grandchildren." In a half-way concession to hundreds of thousands of protesters, Mubarak said in Egypt that he would serve out the rest of his term working to ensure a "peaceful transfer of power" and new rules on presidential elections. His message that he would not immediately leave was rebuffed by many demonstrators in Cairo's main square. Obama warned there would be "difficult days ahead" in Egypt as the situation develops and appealed for calm. Tuesday's developments signaled that after a week of balancing support for protesters and for America's close ally of three decades, the administration had decided that long-term backing for the Egyptian president was no longer tenable. They also coincided with a greater outreach to opposition figures, most notably opening talks with a possible Mubarak successor, Nobel peace laureate Mohamed ElBaradei, a former Egyptian diplomat and chief of the U.N. nuclear watchdog. Officials said that in his conversation with Mubarak, Wisner did not demand that the president step down immediately but rather accept that he was nearing the end of his three-decade grip on power and not try to extend it. Wisner was instructed to use a "light touch" in conveying Obama's message, one official said. Wisner and Mubarak are friends, and the officials said the two had a back-and-forth discussion in which each provided the other with his perspective on developments. The officials said Obama was keenly aware of Mubarak's need to save face and make a graceful exit, acknowledging that the Egyptian leader has been a staunch ally and a major player in all Middle East peace efforts over the past 30 years. The administration hopes that other Arab allies will appreciate that approach, the officials said. The officials spoke on condition of anonymity because they were not authorized to describe the behind-the-scenes diplomacy on the record. On Capitol Hill, Sen. Patrick Leahy, D-Vt., said Mubarak must leave sooner than he plans because his government "has no credibility" to oversee a process toward democracy. "His continued role in Egypt's transition is unrealistic," said Leahy, who sits on a Senate panel that oversees U.S. foreign aid, including some $1.5 billion per year that Egypt receives. Meanwhile, the escalating anti-government protests led the State Department to order non-essential American personnel and their families to leave the country. The department said it had flown about 1,600 Americans out of Egypt since Monday. It said Americans were struggling to reach Cairo's airport because roads were closed as a result of demonstrations. Some 60 U.S. citizens were expected to be flown out late Tuesday, with an additional 1,000 likely to be evacuated in coming days. The Cairo airport is open and operating but the department warned that flights may be disrupted and that people should be prepared for lengthy waits. On Tuesday, it added Frankfurt, Germany, as a destination and the Egyptian cities of Aswan and Luxor as departure points.