WASHINGTON — The Bush administration's faith-based initiative is reaching only a tiny percentage of the nation's black churches, most of which have limited capacity to run social programs, hampering the initiative's promise of empowering those congregations to help the needy, according to a study released this week.

The national survey of 750 black churches by the Joint Center for Political and Economic Studies found that less than 3 percent are participating in the program, which funnels at least $2 billion a year in federal social services spending to religious organizations.

Black churches in the Northeast and those with self-identified progressive congregations and liberal theologies were most likely to be taking part in the program, a finding that surprised the researchers, who concluded that the White House has not used the program as a political tool as some critics have suspected.

"Those people who were most worried can exhale," said Robert M. Franklin, a professor of social ethics at Emory University who worked as a consultant on the survey. "Churches have not been manipulated by Karl Rove. They have not sold out."

Despite instances of grants going to political and ideological supporters of President Bush, the survey found that, overall, liberal-leaning churches were more likely to apply for and receive the grants, even though they tend to view the program more skeptically than their conservative counterparts do.

"The thing is that the churches that are most likely to actually do social outreach or social ministry are liberal churches, they are not conservative churches," said David A. Bositis, a senior research associate at the center who conducted the study. "Those churches may have significant reservations about the program. But if the money is there, they are going to take it. They are the ones who have the capacity and the infrastructure to get grants and administer them."

While many of the churches surveyed had an interest in assisting those in need and frequently offered small-scale programs such as food pantries or used-clothing giveaways, most had neither the money nor the expertise to do more — or even to seek more resources.

Most of the nation's estimated 50,000 black churches are led by pastors who work other jobs full time and have little more than administrative help in running their churches. The survey found that more than one in four black churches had annual revenue of less than $100,000 and half had revenue of less than $250,000. Only 12 percent reported taking in more than $1 million a year.

"The survey reveals for us the breadth of churches in the African-American community, and it shows how churches that already have capacity have a leg up on churches that may do some good things" but are not in a position to do them on a larger scale, said Harold Dean Trulear, a professor of religion at Howard University.