SANAA, Yemen – Tens of thousands of Yemenis demanded the president step down in nationwide protests Thursday, taking inspiration from the popular revolt in Tunisia and vowing to continue until their U.S.-backed government falls.

Yemen is the latest Arab state to be hit by mass anti-government protests, joining Tunisia and Egypt in calls for revolutionary change. The demonstrations pose a new threat to the stability of Yemen, the Arab world’s most impoverished nation, which has become a haven for al-Qaida militants.

“No delays, no delays, the time for departure has come!” shouted protesters, calling for the ouster of President Ali Abdullah Saleh, who has ruled for nearly 32 years.

Saleh’s government is riddled with corruption, has little control outside the capital, and its main source of income — oil — could run dry in a decade.

The protesters were led by opposition members and youth activists in four parts of the capital, Sanaa. In the southern provinces of Dali and Shabwa, riot police used batons to disperse people, while thousands took to the streets in al-Hudaydah province, an al-Qaida stronghold along the Red Sea coast.

In the southern port city of Aden, a 28-year-old unemployed man set himself on fire to protest the economic troubles in the country. The man, identified as Fouad Sabri, was rushed to the hospital in critical condition, medical officials said. The act is the latest in a wave of attempts at self-immolation across the Arab world, which appear to be inspired by events in Tunisia.

A few hundred pro-government supporters held a counter-protest in Sanaa, but they were greatly outnumbered. There were no immediate reports of violence or major unrest in the capital.

The protests calmed by early evening, but organizers said there was more to come today.

“We are pleased to announce that no major clashes or arrests occurred, and the police presence was minimal,” said Mohammed Al-Basha, a spokesman for the Yemeni Embassy in Washington. “The government of the Republic of Yemen strongly respects the democratic right for a peaceful assembly.”