Yemeni officials say at least 16 militants and 12 government soldiers were killed Sunday as troops backed by warplanes and heavy artillery launched a major offensive to retake the al-Qaida-held southern city of Zinjibar.

The attacks pounded areas of Ayban province including the city of Jaar, where al-Qaida has maintained control since March 2011. If the military can reclaim Jaar, it will have surrounded Zinjibar, the provincial capital.

Military sources in Yemen said about 25,000 troops are taking part in the campaign against entrenched al-Qaida positions in Abyan.

The renewed attacks came as U.S. President Barack Obama's top counterterrorism advisor, John Brennan, met Sunday with Yemeni President Abed Rabbo Mansour Hadi in the capital, Sana'a.

Brennan, who also met with the head of Yemen's military, conveyed Washington's strong commitment to support efforts to stabilize the country as it prepares for what the U.S. embassy in Yemen called a “comprehensive national dialogue.”

Mr. Hadi's office said the Yemeni leader briefed Brennan on the army's progress against al-Qaida's branch in Yemen, al-Qaida in the Arabian Peninsula, which Western intelligence agencies say is one of the group's most dangerous affiliates in the world.

Also Sunday, Yemen's Interior Ministry said two of the militants killed in apparent U.S. drone strikes Saturday were Saudi nationals. The two airstrikes killed at least 11 suspected al-Qaida fighters in vehicles traveling in Marib and Shabwa provinces.

Washington has not acknowledged whether the U.S. was behind the attacks. Drone strikes have increased in Yemen's south since Mr. Hadi took power in February.

The attacks come a week after Washington said it had foiled a plot linked to al-Qaida's Yemen-based affiliate to destroy a U.S.-bound airliner using a bomb which could have been undetectable by conventional airport scanners.

A top U.S. senator said Sunday the bomb-maker is thought to have created at least two non-metallic explosive devices, and that he should be killed to safeguard U.S. national security.

Senator Dianne Feinstein told Fox News Sunday she is hopeful “we will be able to – candidly – kill this bomb-maker and kill some of these other associates, because there is a dangerous process in play at the present time.”

The bombs, intended to be smuggled aboard an aircraft undetected and then detonated, bear the forensic signature of suspected al-Qaida bomb maker Ibrahim Hassan al-Asiri, who is believed to be hiding in Yemen.