CAIRO — The long and incendiary reign of Yemeni President Ali Abdullah Saleh showed no sign of ending quietly Monday as fresh bloodshed threatened the nation amid efforts by U.S. and European officials to ease weeks of protest and dangerous political maneuvering that could ignite a civil war.

At least 11 people were killed Monday when police opened fire for the second consecutive day on tens of thousands of protesters in the southern city of Taiz. In the Red Sea town of Hudayda, hundreds of demonstrators were wounded when security forces shot tear gas and bullets to halt a predawn march on the presidential palace.

Yemen is inured to rebellions and tribal violence, but the rising death toll has added an unnerving dimension to Saleh’s brinkmanship. Chaos swells in the provinces, and in the capital, Sanaa, the mood is tense as soldiers clash with demonstrators and an embattled president refuses to relinquish power even as foreign and domestic allies abandon him.

“The concern is that we will replace one oligarchy with another,” said a Yemeni official who asked not to be named. “But Saleh won’t last beyond this year. The U.S. and the Europeans are mediating to facilitate his departure. But the exact timeline will be determined by the opposition and Saleh himself.”

The larger worry, especially among neighboring Saudi Arabia and Western countries, is which tribal or military forces would fill the vacuum to govern a nation confronting deep poverty, a secessionist movement and a resurgent al-Qaida affiliate. Yemen’s strategic location at the crosscurrents of the Middle East and the Horn of Africa has made it a key element in Washington’s counter-terrorism efforts.

The State Department said Monday that the Obama administration has been privately pressing Yemen’s president to step down since anti-government protests began two months ago, despite his collaboration with the United States against violent extremist groups in the country.

Mark Toner, a State Department spokesman, said U.S. Ambassador Gerald Feierstein has been sitting in on the regular meetings of the Yemeni government and opposition aimed at reaching a compromise and a new government.

Opposition leaders and the president have been discussing a deal for the mercurial leader to cede authority to a temporary government until new elections are held. The talks have intensified since at least five top military commanders defected last week. But questions about Saleh’s immunity from prosecution and the fate of his family, including his son and other relatives who run military and intelligence services, have not been resolved.