The protesters are also saying that President Ali Abdullah Saleh's offer to step down in 2013 is not enough.
He has been ruling for nearly three decades and his supporters have also taken to the streets asking people over loudspeakers to join pro-government counter-demonstrations.
Saleh, probably feeling threatened by the unrest spread across the Arab world, had on Feb 2 announced that he would leave office when his term ends in 2013. He also promised that his son would not take over the reins of the government.
US President Barack Obama had called Saleh to express his support for the decision. Yemen's state news agency Saba quoted Obama as saying, "You have handled the situation well, and I look forward to working with you in a good partnership between the two countries."
Yemen is a key ally of the USA in its fight against Al Qaeda.