Witnesses say civilians were also victims of the government actions.
Yemen says its security forces struck al-Qaida positions in Arhab district, north of the capital, and an alleged militant training camp in the southern province Abyan.
Officials say ground troops backed by warplanes launched the offensive to counter what they say were al-Qaida plans to hit Yemeni and foreign targets. Security officials say would-be suicide bombers were among those killed.
Witnesses in Abyan province say civilians, whose homes were mistaken for al-Qaida hide-outs, also died in the raids.
Neither the government nor witness accounts could be immediately confirmed.
University of Sana'a Political Science Professor Ahmed Abdul-Karim Saif believes the offensive is meant to show the government's seriousness in its battle against al-Qaida.
"There are, for a while, an escalation in the activities of al-Qaida in Yemen. And there have been accusations from the West and the international community that Yemen is turning increasingly to be a safe haven for al-Qaida," he said.
The impoverished nation at the southern tip of the Arabian Peninsula has been undergoing a separatist insurgency in the south and a Shi'ite rebellion in the north. Western security officials say the central government's divided focus makes the country an ideal alternative for Afghan-based al-Qaida forces.
The group last month claimed responsibility for an attack in Yemen's Hadramout province that killed at least five government security officers.