CAIRO — By Mona El-Naggar, NYT.

President Hosni Mubarak arrived back in Egypt on Saturday, three weeks after undergoing an operation in Germany, ending a period of intense speculation over the state of his health but maybe not about the future of his country’s leadership.

Mr. Mubarak, who is 81 and has been president since 1981, has “fully recovered,” according to the final medical report issued by the team that removed his gallbladder and a benign growth.

He did not, however, walk down the stairs of the plane. He descended, alongside the first lady, on an escalator. He then walked to shake hands with some of the country’s highest officials, who were waiting to greet him, including the chiefs of the armed forces and intelligence, leading members of his political party, and top Muslim and Christian figures.

Mr. Mubarak flew in to the Egyptian seaside city of Sharm el Sheik, where he is expected to continue to recuperate.

“I have recommended that the president continues his convalescence back home during the coming two weeks before he gradually returns to his full and normal activity,” said Dr. Markus Büchler, who led the medical team that performed the operation, in a televised statement upon releasing Mr. Mubarak from Heidelberg University Hospital on Saturday morning.

Although Mr. Mubarak is now expected to resume full authority of the presidency, it is still not clear how quickly he will be able to manage those responsibilities. The prime minister, Ahmed Nazif, who had been temporarily filling in, is representing Egypt now at a summit meeting of the Arab League in Libya.

In Egypt, power is concentrated in the hands of the president. Because Mr. Mubarak has held the position for almost three decades, it is widely accepted that he will continue to lead the country until he willingly steps down or dies. That is why his recent health crisis amplified the national debate over the question of succession.

“The most important consequence of the operation that Mubarak went through, and his absence from the scene, was to raise again the debate about who should be the future president of Egypt,” said Mustapha Kamel El Sayed, a political science professor at American University in Cairo.

Mr. Mubarak’s fifth term as president ends in 2011, and he has not announced whether he plans to run for another six-year term. He has not appointed a vice president, and there is no clear successor in sight, though it is widely believed that he has been grooming his younger son, Gamal, to be the candidate of the governing National Democratic Party.

In the meantime, there is rising opposition to the prospect of another term for the father or a new term for the son. There are broad demands across the political spectrum for constitutional amendments that would allow for a more democratic process.

At the center of this is Mohamed ElBaradei, the former chief international nuclear watchdog and Nobel Peace Prize laureate. He returned to Egypt last month and embraced a nascent movement led by a group of academics and young activists asking him to run for president.

He made a public appearance on Friday, one day ahead of Mr. Mubarak’s homecoming, by attending the midday prayer at a popular mosque in Cairo.

But according to the Constitution, it is virtually impossible for Dr. ElBaradei or anyone else who is not a member of any party to run as an independent candidate.

Mr. Mubarak’s health, which was always considered a taboo subject, pushed the reality of his age and condition to the forefront of the political debate, although there continues to be a great deal of cynicism regarding the prospect for change now that he has returned home.

“Nothing will change,” said Salama Ahmed Salama, the leader of the editorial board of the independent Egyptian daily newspaper Shorouk. “People thought he might come back from his illness and revise his decisions, but he is coming back stronger than he was before and he will continue to lead without relenting to any of the public demands.”