Tuesday's inconclusive meeting appeared to have delayed a showdown. Hussein also said there are no plans for the group to take to the streets this weekend in protests against the incumbent government, as local media had reported they would.
The move to consider running a candidate appeared to be rooted in the group's frustrations. According to Al-Masry Al-Youm, two of the top names under consideration as possible nominees are Brotherhood strongman and financier Khairat el-Shater and parliamentary speaker Saad el-Katatni. El-Shater, however, faces a legal barrier to running because of a 2008 conviction on money laundering and terrorism charges.
Some observers believe the Brotherhood-military showdown is little more than a smoke screen to conceal a deal to split power. The Egyptian media has speculated for months of a secret deal between them over a so-called "consensus candidate," whom both the Islamists and the military could support.
Another factor in the Brotherhood's possible bid for the presidency is the challenge from an ex-member, Abdel-Moneim Abolfotoh, who was thrown out of the group because he decided to run despite the group's ban. He has drawn support from many of the Brotherhood's young members because of his moderate stances.
The liberals, leftists and youth groups that led the anti-Mubarak uprising are struggling to get their voices heard in the tug-of-war between the military and the Brotherhood.
Their fears deepened this week, after the Brotherhood and ultraconservative Salafis gave themselves a firm majority of seats on a 100-member constitutional panel. That gives the Islamists the strongest hand in writing the new charter, which will determine the balance of power between Egypt's previously all-powerful president and parliament, and define the country's future identity, including the role of religion and minority rights.
More than a dozen mostly liberal and secular-minded members have withdrawn from the panel, saying the committee does not reflect the diversity of Egyptian society. They plan to write an alternative constitution, and many plan to return to street protests. But some liberals are also calling on the generals to intervene.
"It is up to the Supreme Council of the Armed Forced to get involved," said Sameh Ashour, the head of the lawyer's syndicate who resigned from the panel. "We cannot leave representation of Egypt to a majority in parliament."
Associated Press writers Sarah El Deeb and Aya Batrawy contributed to this report.
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