By Tim Ghianni

NASHVILLE, Tennessee (Reuters) - A Tennessee Republican congresswoman survived a spirited primary election challenge on Thursday from an opponent whose campaign was based on opposition to Islam and to a new mosque built near Nashville.

U.S. Representative Diane Black won the primary election by a comfortable margin over Lou Ann Zelenik, noted for her fierce opposition to the Islamic Center built in Murfreesboro, about 30 miles south of Nashville, although it was outside the congressional district she sought to represent.

Zelenik was backed by a wealthy conservative businessman from Nashville, who paid for ads attacking Black over the mosque and Islam. Zelenik charged that Black had not opposed the mosque vigorously.

Zelenik pledged during the campaign that if elected she would "work to stop the Islamization of our society, and do everything possible to prevent Sharia Law from circumventing our laws and our Constitution."

Although Black also opposed the mosque, saying its approval was rushed through, she said she would respect the U.S. constitutional right to freedom of religion.

"Tonight, voters sent a message that they are happy with the way they are being represented in Congress, and I am honored to have their vote of confidence," Black said at her victory celebration.

Black is virtually assured of re-election in November from the rural Tennessee district because no Democrat has entered the race and she faces only token opposition from an independent.

The construction of the Islamic Center near Nashville has been debated for more than two years and a court last month cleared the way for it to be occupied soon by a Muslim congregation.

While the nasty fight between Black and Zelenik got the most attention, another Republican incumbent survived by a much narrower margin.

Chuck Fleischmann, who is in his first term representing the Chattanooga area, won a close three-way Republican primary race over dairy executive Scottie Mayfield, and Weston Wamp, the son of a former Congressman. Although Fleischmann had a conservative voting record, challengers accused him of supporting Democratic President Barack Obama.

Incumbent U.S. Senator Bob Corker, a former Chattanooga mayor and businessman, cruised to victory in the Republican Senate primary. Corker will be heavily favored to win re-election in November, when he will face Democrat Mark E. Clayton.

All other Tennessee members of Congress survived their primaries and will move on to the November general election. Tennessee has seven Republicans and two Democrats in Congress.

(Additional reporting by Andrew Cohen in Washington; Editing by Greg McCune and Jackie Frank)