CAIRO — Egypt geared up Tuesday for a breakneck rush to democracy as its military rulers vowed to hand authority to an elected civilian government in six months and ordered legal experts to draft a revised constitution in 10 days.

The announcements are the latest signal that Egypt’s generals are serious in their pledges to quickly transform the country and relinquish the power they seized when President Hosni Mubarak resigned last week after 18 days of street protests.

Mubarak’s fall has ignited hopes for similar revolutions across the Middle East. On Tuesday, protesters clashed with government supporters in Yemen and Bahrain, suggesting the pro-democracy fervor that began with an uprising in Tunisia and built to a boil in Egypt is continuing to spread.

Some democracy advocates, however, have questioned whether Egypt is moving too fast in implementing the demands of the protesters, noting that it first needs to set up credible political parties, voting laws and other basic campaign rules.

It is not clear precisely when an election will be held. The Supreme Military Council’s statement Tuesday said it hoped to hand over power within six months “to a civilian authority and a president elected in a peaceful and free manner that expresses the views of the people.” The council, which is governing Egypt under martial law, did not specify a calendar for the elections.

Still, the Tuesday announcement is the most specific indication yet of the military’s intentions. Previously, the generals had said that they wanted to step aside in six months but had held out the possibility of ruling until elections could be staged at an indefinite date in the future.

In Washington, President Obama said he was pleased with the Egyptian military’s commitments. “So far, at least, we’re seeing the right signals coming out of Egypt,” he said.