Riots also flared overnight in the southern port of Aden with police shooting to death one demonstrator after cars and a local government building were set ablaze, officials said.
It was the eighth straight day of protests in Yemen inspired by uprisings in Egypt and Tunisia. Demonstrators in the Arab world's poorest country are calling for the ouster of President Ali Abdullah Saleh - a key U.S. ally in fighting al-Qaida terrorists - who has ruled the country for 32 years.
Organizers used social media sites Facebook and Twitter in summoning people to the streets for the "Friday of Rage" following noon prayers, and tens of thousands responded in the capital of Sanaa, the southern port of Aden and the political hotbed of Taiz.
A preacher at the Sanaa University mosque spoke out against torture and beating of demonstrators, telling many protesters who had gathered there: "We have been living for 30 years without purpose or hope."
Imam Jabri Al Yamani admonished the crowd that "protests must be peaceful and not scare and harm the people," but as demonstrators marched toward the presidential palace afterward, the scene descended into violence.
The crowd, chanting anti-government slogans, was met by a heavy deployment of riot police and hundreds of Saleh supporters, similar to confrontations earlier this week. The pro-and anti-government sides attacked each other with rocks, and the riot police began firing in the air and launching tear gas canisters.
At least four people were hurt seriously enough to be taken away by ambulances.
The demonstrators dispersed to other streets, some of which were blocked by police.
Journalists also came under attack by government supporters. An Associated Press reporter saw men wielding sticks attack a TV crew, smashing their camera. Other photographers took refuge in nearby building to avoid the mob.
The U.S. Embassy in Sanaa said it has seen "a disturbing rise in the number and violence of attacks against Yemeni citizens" at peaceful protests.
The statement added that diplomats also saw reports that Yemen government officials "were present during these attacks," which it called "contrary to the commitments that President Saleh has made to protect the right of Yemeni citizens to gather peacefully to express their views."
It urged the government "to prevent any further attacks on peaceful demonstrations and to ensure that all Yemenis, both pro- and anti-government, have equal rights to speech and assembly."
In Taiz, about 270 miles (435 kilometers) south of Sanaa, the call for demonstrations brought out thousands of people, and witnesses said men in a speeding civilian car threw what appeared to be a grenade into a crowd of demonstrators, causing a stampede when it exploded.
At least eight protesters were seriously wounded, and many others were hurt as they fell in the stampede and chaos, said Ghazi al-Samie, a lawyer and activist in Taiz, Yemen's second-largest city.
In Aden, protesters burned four government cars and a local council building in the Sheik Othman neighborhood. Similar government buildings in the Mansoura and Crater districts were set on fire in the past two days.
Later Friday, thousands marched in the city.
A large demonstration also was reported in eastern Hadramawt province, where police fired in the air to disperse protesters.
Saleh, a weak but increasingly important partner for Washington, had pledged not to seek re-election in 2013 or pass power to his son. The promise was seen as an attempt to defuse calls for his ouster.
Opposition groups said they are suspicious of Saleh's offer and want concrete proposals for change.
Yemen has become a main battleground against al-Qaida. The government, which receives millions of dollars in U.S. military aid, has allowed American drone strikes on al-Qaida targets and has stepped up counterterrorism cooperation.
The U.S.-born radical cleric Anwar al-Awlaki, thought to be hiding in Yemen, is believed to have inspired and even plotted or helped coordinate recent attacks on the U.S. Those include the failed December 2009 bombing of a Detroit-bound airliner and the unsuccessful plot to send mail bombs on planes from Yemen to the U.S.
Al-Awlaki also is believed to have inspired the deadly 2009 shooting rampage at Fort Hood, Texas, and had ties to some 9/11 hijackers.
Nearly half of Yemen's population lives below the poverty line of $2 a day and its government is riddled with corruption. The country also is plagued by shrinking water and oil resources and an inability to feed its people.
Tens of thousands have been displaced by conflict. The country is wrestling with a lingering tribal uprising in the north and a secessionist movement in the south.