The fighting took place in an al-Qa'ida stronghold in western Yemen, haven for a group that attacked the US embassy in the country in 2008, killing 10 Yemeni guards and four civilians. A government statement said at least one suspected militant was arrested.
"The (Interior) Ministry will continue tracking down al-Qa'ida terrorists and will continue its strikes against the group until it is totally eliminated," Deputy Interior Minister Saleh al-Zawari told senior military officials at a meeting in Mareb, another province believed to shelter al-Qa'ida fighters.
The attack came as US officials said the Pentagon was drawing up urgent plans for increased military co-operation with Yemen, including possible retaliatory strikes against al-Qa'ida targets.
He acknowledged, however, that Yemen would need technical and intelligence information to carry out such attacks, and senior Pentagon sources said fresh target lists were being drawn up in case US President Barack Obama called for them.
The US has never publicly acknowledged the rapid build-up of its military presence in and near Yemen since last year but sources say that attacks already mounted by Yemeni government forces on al-Qa'ida training camps would have been impossible without American hardware and know-how. Future strikes could involve the use of US drones, fighter jets and ship-launched cruise missiles.
The US military has formidable firepower on permanent standby in the form of carrier battle groups stationed in Bahrain, and unimpeded access to Yemen from bases in Djibouti and the Indian Ocean island of Diego Garcia.
Pinpointing those who groomed Umar Farouk Abdulmutallab for his suicide mission in the Arab world's poorest country will not be easy but the movements of known militants and the would-be bomber's responses to interrogators have provided leads.
Two former inmates of Guantanamo Bay detainee camp who were returned to Yemen via Saudi Arabia in 2007 are thought to have assumed the leadership of al-Qa'ida in the Arabian Peninsula, the group that claimed responsibility for the attempted airline bombing.
Muhammad al-Awfi and Said Ali al-Shihri are believed to have been the targets of a pair of airstrikes on suspected terrorist training camps in the east of the country before Christmas that the Yemeni government says killed more than 60 militants. Reports that the pair were killed on Christmas Eve have not been confirmed.
The AQAP leadership was the target again yesterday in the raids by Yemeni forces.
Abdulmutallab has reportedly told his FBI interrogators in Michigan that he attended a gathering of young men "all covered up in white martyrs' garments" in Yemen shortly before he left the country.
The American response to the near-catastrophe over Detroit has veered from casual reassurance to angry recrimination and thinly veiled threats of military action in less than a week.
US investigators said Abdulmutallab told them he received training and instructions from al-Qa'ida operatives in Yemen.
Yemen's government has said Abdulmutallab spent two periods in the country, 2004-2005 and from August to December of last year, just before the attempted attack.
Yesterday's clashes took place in Hudaydah province, an al-Qa'ida stronghold along the Red Sea coast. A security official said the target was a house owned by an al-Qa'ida sympathiser. The official said the owner was arrested, a suspected al-Qa'ida member was injured and several militants who fled were being pursued.
Before yesterday's clashes, Yemeni forces backed by US intelligence carried out two major strikes against al-Qa'ida hideouts, reportedly killing more than 60 militants.