Police and protesters are doing battle in Cairo, as large demonstrations of Islamist political factions call for democratic reform and the end of post-Mubarak military rule.

Police sprayed tear gas and swung batons in an attempt to clear the square, one day after a massive demonstration calling for open elections. Violence went both ways, CNN reported: police shot off tear gas and warning shots as thousands of protestors tossed rocks and Molotov cocktails and at one point "torched a police van."

"We sent hundreds of Central Security Police Forces and forced out the remaining several hundred protesters who refused to go home. We arrested four thieves and thugs who acted aggressively and beefed up security in and around square overnight," interior spokesman Alaa Mahmoud said earlier Saturday.

The Friday throng, dominated by Islamist parties but including secular protesters as well, turned out ahead of upcoming parliamentary elections set to begin on November 28.

Mahmoud said the "Islamists and revolutionaries had left as they promised not have a sit-in." But stragglers remained, and he said many of the people who stayed in the square were families of those injured during the upheaval earlier this year that led to President Hosni Mubarak's departure from office.

Egypt has since been ruled by the Supreme Council of the Armed Forces. The military said it wants to transfer power to a civilian parliament and president.

The Wall Street Journal's Tamer El-Ghobashy is live tweeting the conflict from Tahrir Square. It's a fascinating and scary feed; he's seeing blood, fighting off the effects of tear gas, and also documenting the surreal touches of an impromptu urban battle, like a cotton candy vendor standing incongruously in the middle of a riot.

Reuters has video of police attempting to clear the square on Saturday:

Writing for The New Yorker, Wendell Steavenson reports the reaction of some locals in Cairo to the massive demonstration force that Islamist parties have managed to turn out in Cairo. The upshot: "The intellectuals have lost."

My liberal Egyptian acquaintances roll their eyes at America’s recent diplomatic, conciliatory remarks about working with moderate Islamists in the wake of the Arab Spring. “You can’t trust them,” they say. Some liberals have decided that it’s perhaps better to go along with the Supreme Council’s efforts to push through a preemptory Constitution, as an end-run around an Islamist-dominated parliament. Increasingly, Egyptian politics feels like a three-way tug of war.

There's disdain for the Americans' position on Egypt on this side of the ocean, too. Jennifer Rubin, who blogs at Right Turn for The Washington Post, warns that the Obama administration "seems determined to toss away even that minimal influence" that it now has over Egypt's military ruling council — namely the U.S. funding that shores up the country's armed forces.

Evening update: Yes, things are really bad in Cairo, according to The New York Times.

The clashes began midday Saturday when the police tried to clear out the last remnants of a large demonstration in Tahrir Square the day before. That demonstration, organized by Islamists but appearing to represent a far broader cross-section of Egyptians, drew tens of thousands of people calling for a swift end to military rule.

After news circulated that the security forces had moved in to force out a few hundred protesters who had spent the night, thousands of others stormed into the square to defend it, setting off battles that spread across downtown Cairo into the night.

Protesters threw rocks at police vehicles, capturing a police truck and passing out handcuffs, hats and other gear found inside. Others smashed the sidewalk into rocks to hurl at the police, and threw Molotov cocktails. Plumes of black smoke from a burning police truck wafted through the white clouds of tear gas that floated along the Nile.