Yemen's embattled president has failed to pacify protesters with plans to draw up a new constitution.
Thousands poured onto the streets of the capital Sanaa to demand that he step down after 32 years in power.
Under his plan the constitution would guarantee the independence of parliament and judiciary.
The demonstrators have set up protest camps in Sanaa and the cities of Aden and Taiz, saying they will not leave until US-backed President Ali Abdullah Saleh does.
The opposition promptly rejected Saleh's latest offer.
Saleh, an ally in the Obama administration's fight against al Qaida, has been making a series of concessions to head off a movement seen as one of the most serious threats to an Arab government inspired by uprisings in Tunisia and Egypt.
He told thousands of supporters gathered at a stadium in Sanaa that a new constitution would be drafted by the end of year establishing the separation of legislative and executive powers. The president currently controls all other branches of government.
Saleh said he ordered the government to "fulfil the demands of the youth camping in Sanaa, Aden and Taiz and in other cities but without sit-ins or chaos."
Shortly after Saleh finished his speech, some 4,000 people, mostly students, took to the streets and headed toward the main square in Sanaa, calling for his downfall.
Also in the capital, some 5,000 doctors, nurses, pharmacists and medics from all over the country, marched toward the central square, wearing their white robes and protesting this week's shooting by army troops of anti-government protesters gathered at Sanaa University.
Opposition leader Yassin Said Numan said Saleh's initiative came too late.
"The president's initiative has been overtaken by events and facts on the ground today, but if it came six months ago, the matter would be totally different," Numan said.
Saleh pledged in his address that Yemen would hold general elections and form a new government by early 2012.Reuse content