At least three people were injured as the rivals pelted each other with stones, said an AFP correspondent, in the fourth straight day of protest in central Sanaa.
Inspired by uprisings in Tunisia and Egypt, protesters - estimated to number 3,000 - poured out of Sanaa University to demand the resignation of president Ali Abdullah Saleh, who has been in power for 32 years.
"The people want to oust the regime" they chanted, picking up the slogan used by demonstrators in Egypt who forced president Hosni Mubarak to step down last Friday after 18 days of mass protests.
As they advanced on Mr Saleh's palace, supporters of the president's General People's Congress armed with batons and stones confronted the demonstrators, who responded by hurling stones.
The president's supporters tried to attack opposition MP Ahmed Saif Hashed, who took part in the protest, but he was protected by fellow marchers, witnesses said.
Demonstrators said police sided with the pro-Saleh militants in dispersing the crowd.
International human rights watchdogs have criticised the conduct of the police, including the alleged use of Tasers.
But cyber-activist Hashem al-Abara, involved in organising the protests in the Arab world's poorest country through Facebook, said the demonstrators would not be intimidated.
"We will continue with the protests and the ruling party's attacks against our peaceful demonstrations will not set us back," he said.
"If Egypt stayed 18 days, it will not matter to us if we stay one, two or three months."
As tensions soared outside his palace, Mr Saleh announced his office was open "to listen to the views" of "various segments of society from all the republic's provinces".
On Monday, rocks and batons flew in the capital as the protesters - mainly students and lawyers - clashed with police and Mr Saleh's supporters. Police also attacked protesters in Sanaa on Sunday.
In Taez, south of Sanaa, where anti-Saleh demonstrators staged protests on Tuesday for a fourth day, similar clashes erupted with regime loyalists, with no casualties reported after eight people were hurt on Monday.
The Paris-based media rights group, Reporters Without Borders (RSF), condemned attacks on journalists covering the protests.
"RSF roundly condemns the attacks that security agents, police officers and plainclothes men have carried out against journalists covering street protests in Sanaa during the past two days," it said.
It urged "Yemeni authorities to allow journalists to do their work without fear of being arrested or physically attacked by members of the security forces, who are supposed to protect them".
Anger at rampant corruption has helped to fuel unrest in Yemen.
In Sanaa, protests have become increasingly violent, despite Mr Saleh - elected to a seven-year-term in September 2006 - urging dialogue on forming a government of national unity.
Besides poverty and unemployment, Mr Saleh's government is grappling a secessionist movement in the south, rebellion in the north, and a regrouping of Al Qaeda on its soil.