The liberals and secularists who formed the core of the Egyptian revolution are now scrambling to stave off political gains by the Muslim Brotherhood, a once-outlawed organization that is widely expected to become the dominant force when a new parliament is elected.

Concern about the group’s political ambitions was heightened this week when a prominent member of the Brotherhood signaled that he would run for president as an independent, a move that cast doubt on the Brotherhood’s contention that it intended to sit out this year’s presidential race.

The Brotherhood, however, has said that it intends to mount a vigorous campaign in parliamentary elections expected to take place in September, two months ahead of the presidential vote.

Prominent liberals and secularists say they are deeply worried about what might happen if the Muslim Brotherhood makes a strong showing. Some are pushing for changes, including the postponement of parliamentary elections, which could level the playing field by giving other parties more time to organize.

“It’s not a fair fight,” said Naguib Sawiris, the second-wealthiest man in the country and one of the founders of the Free Egyptians Party, which is promoting liberal and secular policies.

He said his well-funded party could not reasonably compete with the Brotherhood, which has had 80 years to build a robust network of operatives and supporters across Egypt. The entrepreneur also said investors are squeamish at the prospect of a new government in which the Muslim Brotherhood would play a leading role.

“They have substituted the dictatorship of Mubarak with the dictatorship of the Muslim Brotherhood,” Sawiris said. “That’s where Egypt is going now.”

Amr Moussa, a leading candidate for the presidency, said in a recent interview that there is “enough time to perhaps reconsider” the current election schedule. He said that the presidential election should be held before the parliamentary contests, to give the president more influence over the drafting of a constitution.

Mohamed Saad el-Katatny, a Muslim Brotherhood leader who once headed the group’s parliamentary bloc, said he didn’t think the timing of the elections was likely to affect the outcome.

“For us the timing of the election does not make a difference,” he said in an interview. “But being late is not in anyone’s interest, and it might make it too late to have a peaceful transition of power.”

Although the Brotherhood has long advocated that Egypt should become an Islamic state ruled according to a dogmatic interpretation of sharia law, party members have sought in recent months to portray the group as being more progressive and inclusive than critics give it credit for. They rebranded the political wing of the movement the Freedom and Justice party and have formed allegiances with some secular and Christian politicians.

Brotherhood leaders have also pushed back on criticism that they are being underhanded about their political ambitions. Skepticism about their plans was certain to increase following Thursday’s announcement by prominent member Abdel Moneim Abou el-Fotouh, who told the Reuters news agency that he intends to run for president.

The Muslim Brotherhood said in a statement on its Web site that it had no prior knowledge of his intention to seek the presidency and that he would not be running as a representative of the group.

Egypt is in the midst of reinventing its political system, with new political parties announced almost every day. The military council running the country — which makes its important policy announcements on its Facebook page — has yet to post anything definitive about the timing of elections.

But the balance of power between parliament and president won’t be resolved until a new constitution is drafted, sometime after the parliamentary elections. And some of the liberals and secularists who demanded an end to the pharaonic powers that Mubarak commanded during his 30-year rule are now talking about the need to shore up a future Egyptian president against the prospect that parliament would be controlled by Islamists.

“The liberals are confused,” said Mokhtar Nouh, a former member of the Muslim Brotherhood who split with the group almost a decade ago because of philosophical differences. A powerful parliament would almost certainly mean a more powerful Muslim Brotherhood, Nouh said, “because they are the ones who are ready.”

For the moment, Cairo feels a little like Schoolhouse Rock, with workshops about how to write a constitution popping up on every street corner. But like much about the revolution, the practical questions that arise about how to reshape the country are rarely as simple as the principles that undergird them.

For example, many Egyptians now support the long-hated emergency law that gives police extensive powers to detain people without charges or trial, because they fear for their security. And a Pew poll released last month found broad support for both the Muslim Brotherhood and the secular activists who set off the revolution — two groups that agreed about the need for change but little else.

There remain prominent defenders of a weaker president. One is the likely future head of the Arab League, Mostafa al-Fiqqi, whose nomination is opposed by many protesters who think he was too close to Mubarak, an allegation he denies.

“We have this tradition of the pharaoh,” al-Fiqqi said. “It’s a one-man show . . . the parliamentary state would work best.”

Nabil Fahmy, dean of the School of Public Affairs at the American University in Cairo and a former ambassador to the United States, said the organizational strength of the Muslim Brotherhood would give it the upper hand in parliament, at least intitially.

“We haven’t had enough time for the parties to mature,” Fahmy said. He said he believes that the next Egyptian president needs to wield considerable power, in a system that might emulate that of France. But he also said he favors a strong parliament.

“It’ll be much better than in the past,” Fahmy said of the evolving political structure, “but I’m not sure it’ll be as good as we’d want it to be.”

Special correspondent Sherine Bayoumi contributed to this report.