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Yemeni security forces have swept into a region of the country thought to be a haven for al Qaeda, the governing party says.

More than 1,000 soldiers and security officials are involved in the operation in Shabwa province, the al-Motamer party said on its website Saturday.

The United States believes Yemeni-American militant cleric Anwar al-Awlaki is in the region. The cleric has been linked to Fort Hood shooting suspect Maj. Nidal Hasan and failed Christmas bomber Umar Farouk AbdulMutallab.

The offensive comes after the governor of the province delivered an ultimatum to local tribes to "eradicate" al Qaeda operatives themselves or the army would move in, a Yemeni government official told CNN Sunday.

The result was a joint operation between the tribes and the army, said the official.

"The tribes decided to start trying to hunt for al Qaeda operatives with help from Yemen's security forces and the operation that started last night was the tribes' first terror sweep in the mountains of Shabwa. They went hiking and army units joined them. They also had air support," the source said.

Yemeni officials have said in the past that if al-Awlaki is captured, he will not be extradited to the United States because the country's constitution forbids sending Yemenis abroad to face trial.

"He's not a problem for Yemen," Yemen's counterterror chief, Gen. Yahya Saleh, told CNN earlier this month. "He's a problem for America."

Yemen believes there are about 400 al Qaeda elements in Yemen, including Saudis who "plot to entice chaos and destruction in several places in the country," Yemeni Foreign Minister Abu Bakr al-Qerbi said on the party's website Sunday.

Yemen has become a key battleground for al Qaeda since a local affiliate calling itself al Qaeda in the Arabian Peninsula was established in 2009.

Top U.S. counterterror official John Brennan visited the country recently to assure it of Washington's support.

Security forces are combing the Awalek region of Shabwa province for al Qaeda suspects, local journalists told CNN Sunday. The region is the home of Anwar al-Awlaki's tribe.

Yemen also carried out an offensive against al Qaeda in the area last month, after which the group retaliated against a government convoy. Another offensive was launched in the southern province of Abyan last weekend.

U.S. officials say al-Awlaki helped recruit AbdulMutallab, the Nigerian man charged with trying to blow up a Northwest Airlines trans-Atlantic flight as it landed in Detroit, Michigan, on Christmas Day.

Al-Awlaki is also said to have exchanged e-mails with Hasan, the accused Fort Hood shooter.

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