The larger of the two groups called for the end of Saleh's 32-year rule.
"Get out get out, Ali. Join your friend Ben Ali," the crowds chanted, comparing Saleh to Tunisia's ousted President Zine El Abidine Ben Ali.
Another smaller group however wanted him to stay in office.
The protest turned violent after police fired tear gas at the students. According to security officials some 30 protesters were also detained during the turmoil.
Saturday's demonstration, which was confined to the grounds of the University of Sanaa, is considered as the first major public challenge to the Yemeni president.
Protests have been witnessed in major Yemeni cities since the Tunisians overthrew their president earlier this month.
However, calling for President Saleh's ouster had been a red line that few protesters dared to test.
One of the rally organizers, lawmaker Fouad Dahaba, said the demonstration was only a beginning and they will not stop until their demands are met.
"We will march the streets of Sanaa, to the heart of Sanaa and to the presidential palace. The coming days will witness an escalation," the Associated Press quoted Dahaba as saying.
People in Yemen are angry about increasing commodity and fuel prices.
They are also enraged at a controversial constitutional amendment, approved by Yemen's parliament on January 1, which could see President Saleh rule for life.
In an attempt to cool public outrage, last week, Saleh suspended the country's oil minister and slashed state workers' income tax rates by up to fifty percent.
However tensions seem to persist in the impoverished conflict-riddled country.
Activists say the revolution in Tunisia is an epoch-making change which threatens the existence of dictatorial regimes in the Arab world.
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