Medics in Aden, meanwhile, said three demonstrators were shot dead as police dispersed protests in several areas of the southern port city, which has borne the brunt of the 10 killed in clashes which broke out in Yemen last Sunday.
The grenade attack came as hundreds of protesters took to central Taez after the weekly Muslim prayers to demand President Ali Abdullah Saleh's ouster, in protests that have been raging in the city for the past week.
A local official told AFP the grenade was lobbed at protesters from a speeding car with government number plates. Two people were in the car "but we will not identify their political affiliation," he said.
Two people were killed and 27 wounded, a medical official in the southern city told AFP.
In the capital Sanaa, the scene of a sixth straight day of demonstrations, at least four anti-regime protesters were wounded in an attack by Saleh partisans, witnesses said.
Several journalists were severely beaten by supporters of the ruling General People's Congress (GPC) who attacked the demonstration using batons and axes, an AFP correspondent reported.
Thousands of demonstrators, mostly students, had gathered following the weekly Muslim prayers in a main street of Sanaa. "People want to overthrow the regime," they chanted.
Saleh's supporters numbered in the hundreds, aided by security agents in plainclothes.
Students have tried for the past week to hold a protest march toward the presidential palace but been intercepted each day by stone-throwing regime supporters armed with batons.
The US embassy in Sanaa on Friday condemned "a disturbing rise in the number and violence of attacks against Yemeni citizens gathering peacefully to express their views on the current political situation.
"We have also seen reports that government of Yemen officials were present during these attacks," it said on the embassy website, urging authorities "to prevent any further attacks on peaceful demonstrations."
In Aden, three people were shot dead as police dispersed anti-regime protests, medical sources told AFP. The deaths occurred in the Khor Maksar, Sheikh Othman and Al-Saada districts of the city.
Three more people were shot dead and 19 wounded on Thursday as security forces clashed with protesters in Aden, according to a casualty toll from an official at Jumhuriah hospital.
Police opened fire on thousands of demonstrators who marched in Aden's Al-Mansura neighbourhood demanding the ouster of Saleh, who has been in office for 32 years.
The demonstrators, chanting, "Ali, out," damaged shops, set fire to tyres and placed obstacles in the streets to block traffic, an AFP correspondent said.
Police fired tear gas and then live rounds to disperse the protesters, who responded by throwing stones.
The latest deaths raised to 10 -- eight in Aden and two in Taez -- the number of people killed in Yemen, the Arab world's poorest country, since the wave of unrest broke out on February 13.
In Sanaa, protests have becoming increasingly violent, despite Saleh -- elected to a seven-year-term in September 2006 -- urging dialogue on forming a government of national unity.
Amnesty International on Friday issued a fresh condemnation of the violence.
"Yemeni authorities seem to be stepping up their crackdown on protesters and we are gravely concerned that if that continues, the death toll will inevitably rise," it said in a statement.