More than 20,000 anti-government protesters gathered in the Yemeni capital, Sanaa, for a "day of rage" against President Ali Abdullah Saleh.
The demonstrators called for a change in government and rejected Mr Saleh's offer to step down in 2013 after more than 30 years in power.
Meanwhile, a similar number of his supporters rallied in a central square.
The gatherings are the largest in two weeks of protests inspired by the popular uprisings in Tunisia and Egypt.
In an emergency parliament session on Wednesday, Mr Saleh, 64, laid out his plans to move aside, saying he would not seek to extend his presidency when his current term expires in 2013 and pledging not pass on power to his son.
Despite his call to protesters to cancel their planned rallies, both pro- and anti-government demonstrators gathered in different parts of Sanaa.
"The people want regime change," anti-government protesters shouted as they gathered outside Sanaa University. "No to corruption, no to dictatorship."
The so-called "day of rage" was organised by civil society groups and opposition leaders who complain of mounting poverty among a growing, young population and frustration with a lack of political freedoms.
Unemployment in Yemen runs at 40%, and there are rising food prices and acute levels of malnutrition.
The country has also been plagued by a range of security issues, including a separatist movement in the south and an uprising of Shia Houthi rebels in the north.
There are fears that Yemen is becoming a leading al-Qaeda haven, with the high numbers of unemployed youths seen as potential recruits for Islamist militant groups.
The pro-Saleh supporters rallied in Sanaa's central Tahrir (Liberation) Square. They carried banners saying: "Yes for development, yes for stability, no for chaos."
The pro-government supporters are also calling for political and economic reforms, but they believe only Mr Saleh can guarantee the security and stability of the country, and they do not want him to step down now, says the BBC's Lina Sinjab in Sanaa.
But they say they will keep up their street protests until Mr Saleh delivers on the promised reforms, our correspondent says.
There were initial fears that violence could break out on Thursday, but the protests ended peacefully by mid-morning, she added.
President Saleh, a Western ally, became leader of North Yemen in 1978, and has ruled the Republic of Yemen since the north and south merged in 1990. He was last re-elected in 2006.
In January, he had proposed a constitutional amendment that would allow him to stand for re-election in the next presidential ballot in two years' time.
But after the revolt in Tunisia, which forced the country's president to flee into exile, he has publicly stated that he is opposed to hereditary rule. There has been widespread suspicion that was grooming his eldest son, Ahmed Saleh, who commands an elite unit of the Yemeni army, to succeed him as president.
Mr Saleh has also made a series of other concessions - halving income tax, ordering his government to control prices, and pledging to raise the salaries of civil servants and military personnel by around $47 (£29) a month.