ADEN, Yemen — At least 11 people were killed in Yemeni army operations against al-Qaida-linked militants on Wednesday, including an offensive in eastern Yemen, where fighters had declared their aim to set up an Islamist state.

President Abd-Rabbu Mansour Hadi, struggling with an Islamist insurgency, a separatist movement in the south, and a spate of attacks by gunmen on government targets, praised the military operations.

"What you did today . . . reinforces our confidence in your ability to pursue the remnants of the terrorist elements of al-Qaida until they are uprooted," Hadi said in a message to the armed forces.

Three soldiers, including the force commander, and at least seven militants, were killed in fighting at Ghail Bawazeer, north of the Hadramout provincial capital of al-Mukalla, a Yemeni military source said.

The Yemeni Defense Ministry said only one officer was killed and five soldiers wounded in the fighting in which troops were backed by tanks and helicopters. The ministry said seven militants died and several others were wounded.

One civilian traveling on bus that was caught in the crossfire was killed and at least two others wounded, locals said.

In a separate incident, the army killed a local al-Qaida leader and a member of the group and captured a third in the central province of Marib, state news agency Saba reported.

The unrest has alarmed neighbouring Saudi Arabia, the world's leading oil exporter, as well as the United States, which views Yemen as a front line in its fight against al-Qaida.

The Yemeni army last year drove out Islamist militants from several towns they had captured a year earlier in southern Yemen, in an offensive backed by the United States.