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Mr. Saleh, a weak but increasingly important partner for Washington, had pledged not to seek re-election in 2013 or pass power to his son. The promise was seen as an attempt to defuse calls for his ouster.

Opposition groups said they are suspicious of Saleh’s offer and want concrete proposals for change.

Yemen has become a main battleground against al Qaeda. The government, which receives millions of dollars in U.S. military aid, has allowed American drone strikes on al Qaeda targets and has stepped up counterterrorism cooperation.

The U.S.-born radical cleric Anwar al-Awlaki, thought to be hiding in Yemen, is believed to have inspired and even plotted or helped coordinate recent attacks on the U.S. Those include the failed December 2009 bombing of a Detroit-bound airliner and the unsuccessful plot to send mail bombs on planes from Yemen to the U.S.

Mr. al-Awlaki also is believed to have inspired the deadly 2009 shooting rampage at Fort Hood, Texas, and had ties to some of the 9/11 hijackers.

Nearly half of Yemen’s population lives below the poverty line of $2 a day and its government is riddled with corruption. The country also is plagued by shrinking water and oil resources and an inability to feed its people. Poverty and malnutrition are rampant in the country’s rugged hinterlands.

Tens of thousands have been displaced by conflict. The country is wrestling with a lingering tribal uprising in the north and a secessionist movement in the south.