Violence erupted in Egypt's capital when supporters of President Hosni Mubarak clashed for the first time with protesters, as the regime dug in against demands, from within the country and from Washington, that a transfer of power begin immediately.

The clashes began hours after Mr. Mubarak announced in a speech late Tuesday that he wouldn't run in elections slated for later this year. They gained intensity during the day in central Cairo's Tahrir Square, with the two sides rushing at each other, wielding clubs and throwing...