The expanded operations included intensified overnight airstrikes and ground military raids against the al-Qaida hideouts in the mountainous areas of al-Bayda and southeastern province of Shabwa.
The US military is trying to verify reports that it has killed one of the men behind a deadly attack on the USS Cole in Yemen in 2000.
"US forces are still assessing the results of the strike following a deliberate process to confirm his death", said Captain Bill Urban, a spokesman for US Central Command.More news: Daenerys meets Sansa in new Game of Thrones teaser
The militant, said to be an al-Qaeda commander, was on the FBI's most wanted list over the attack on the warship.
It wasn't revealed whether the operation was carried out by the CIA or by USA military forces, only that the airstrike was the result of a joint U.S. military and intelligence operation, a United States administration official told CNN.
In 2003, a grand jury indicted Al-Badawi with 50 counts of various terrorism charges, including the murder of USA nationals and military personnel.More news: Walton: Lakers needs 'more passion' from Ball, Ingram
The Cole, a guide-missile destroyer, was attacked by suicide bombers in an explosives-laden boat while refueling at the Yemeni port of Aden. He was sentenced to death but his sentence was later reduced to 15 years in prison, the Associated Press reported.
Following his escape from prison in 2003, Badawi was captured by Yemeni authorities in March 2004 but CBS reported the Federal Bureau of Investigation as saying he managed to escape again in February 2006 after he and other inmates dug a tunnel that led from the prison to a nearby mosque. He subsequently surrendered to Yemeni authorities in October 2007, but was freed under certain conditions, including a pledge of allegiance to Yemeni President Ali Abdullah Saleh.
Al-Badawi, who was 55 or 58 years old, was killed on Tuesday when US forces carried out a precision airstrike in Ma'rib province, which is located to the northeast of Yemen's capital, Sana'a.More news: Gabonese Military Overthrows President Ali Bongo
The strike took place when al-Badawi was reportedly driving alone.