A military official, who would not be named, said there had been three attacks on the house and one on an orange grove near the village where the authorities think al-Shabwani had built a safe haven for dozens of Al-Qaeda in the Arabian Peninsula members.
The official said that there had been a large deployment of government forces at the city of Maarib, about five kilometres from Erq al-Shabwan.
Orange grove targeted
During the afternoon, witnesses said, jets twice fired missiles at the orange grove and afterwards continued to fly in the area.
Mohamed Vall, reporting from the southern city of Aden, said quoting the Yemeni army website that one al-Qaeda member was killed in a separate clash with security forces in Lahij, about 50km north of Aden.
"The fighting took place after a government vehicle was hijacked by al-Qaeda and there was an exchange of fire between the two sides in which the member of the group was killed," he said.
The clashes come just days after Yemen said it had killed six suspected leaders, including al-Shabwani, of Al-Qaeda in the Arabian Peninsula in Saada, a province north of Saana.
Describing Wednesday's air assault in Maarib, our correspondent said: "[The air raids] started around noon. The government said they targeted the home and farm of al-Shabwani."
"There were four raids in that area. The government said there was an exchange of fire and that al-Qaeda members were armed with anti-aircraft weapons, which they tried to use against the government aircraft. But the government did not talk about any al-Qaeda casualties."
In this context, our correspondent noted that al-Qaeda in the Arabian Peninsula had rejected the Yemeni government's claim about al-Shabwani's death, and that the government had not commented on al-Qaeda's denial.
Airline plot connection
Yemen is under US pressure to clamp down on Al-Qaeda in the Arabian Peninsula, which claimed responsibility for the December 25 bid to blow up a US flight from Amsterdam as it landed in Detroit.
Wednesday's air raid comes a day after the United Nations Security Council added Al-Qaeda in the Arabian Peninsula to its list of outlawed organisations.
Two of the group's purported leaders, Nasser al-Wahayshi and Qasim al-Raymi, face new restrictions after the move by the Security Council's sanctions committee.
The sanctions against the two men, who were among 23 fighters who escaped from a jail in Sanaa in 2006, include worldwide freezes on their assets and travel bans.
"Today's actions strengthen international efforts to degrade the capabilities of AQAP," Susan Rice, the US ambassador to the UN, said on Tuesday, referring to Al-Qaeda in the Arabian Peninsula.
Al-Qaeda in the Arabian Peninsula was formed in January 2009 after the merger of groups in Saudi Arabia and Yemen.
It has since set up bases inside Yemen and has been blamed for the suicide attack on South Korean tourists in March 2009 and an attempt to assassinate the Saudi deputy interior minister across the border.
The UN committee made its decision shortly after the US state department added the Yemen-based group to it list of proscribed organisations.
"We are determined to eliminate AQAP's ability to execute violent attacks and to disrupt, dismantle, and defeat their networks," Philip Crowley, a state department spokesman, said.