By focusing on centrist and more liberal evangelicals, who have been pushing the movement to broaden its agenda beyond traditional social issues, Mr. Obama is hoping to chip away at a margin that has favored Republicans. His campaign selected Ohio to announce the plan, a state where Mr. Bush engaged in a sprawling voter turnout effort among evangelicals.

Mr. Obama’s proposal was met with praise from leaders like the Rev. Jim Wallis, a prominent spokesman for more liberal evangelicals. Mr. Wallis applauded the fact that Mr. Obama, as a Democrat, was willing to talk about his Christian faith and “wants a faith-based program that’s even better than the Bush program.”

Several former Bush administration officials who had a hand in shaping the current policy, including John J. DiIulio Jr., director of Mr. Bush’s Office of Faith-Based and Community Initiatives in 2001, also applauded Mr. Obama’s proposal. Though the program is widely associated with Mr. Bush, similar ideas have been supported by Democrats.

“His plan reminds me of much that was best in both then-Vice President Al Gore’s and then-Texas Gov. George W. Bush’s respective first speeches on the subject in 1999,” Mr. DiIulio said.

But the Rev. Barry W. Lynn, executive director of Americans United for Separation of Church and State, criticized Mr. Obama’s support of a program that Mr. Lynn said had undermined civil liberties and civil rights. “I am disappointed that any presidential candidate would want to continue a failed policy of the Bush administration,” Mr. Lynn said. “It ought to be shut down, not continued.”

In one example of how he would use the approach to carry out a policy goal, Mr. Obama proposed $500 million per year to provide summer education for one million poor children, with a goal of closing the achievement gaps between wealthy students and poorer ones. The campaign did not provide a cost proposal for the full program, but said the educational piece could be financed by reducing the growth in the federal travel budget and streamlining the management of surplus government property.

If elected, Mr. Obama said, he would call for a pre-inauguration review of all executive orders pertaining to the religion-based program, particularly those dealing with hiring. The program would “be central to our White House mission,” he said, and would consider elevating the director of his Council for Faith-Based and Neighborhood Partnerships to a cabinet-level post.