Muslims tended to lean Republican as recently as 2000, but a backlash after the Sept. 11, 2001, attacks, along with the Middle East policies of the George W. Bush administration, has led to a gradual shift toward the Democrats. A Pew Research Center survey last year found that 70 percent of American Muslims identify with the Democratic Party, while just 11 percent consider themselves to be Republicans.

Although Muslims make up only about 1 percent of the population in the United States, civil rights groups have set a goal of registering a million new voters. Efforts will be focused on swing states such as Ohio and Florida that have large Muslim populations, potentially giving the small but united voting bloc the power to tilt close elections.

“The best answer to this anti-Muslim rhetoric is engagement in the political process,” said Naeem Baig, the president of the Islamic Circle of North America. “It is a matter of survival for the American Muslim community.”

Like many Muslims, Mr. Baig said that the vitriol directed at Americans who practice Islam is the worst that he can remember. Violence against Muslims and attacks on mosques increased last year, and Muslim parents say their children are being bullied at school. Even the voter registration push has drawn criticism in some circles, with websites such as Creeping Sharia lamenting greater Muslim engagement in American politics and suggesting that “the problem with CAIR’s initiative is that no one who follows the Quran can honestly claim to follow the Constitution.”