By Dan Gilgoff, CNN

President Barack Obama signed an executive order Wednesday clarifying the ground rules for religious groups partnering with the federal government through the White House's controversial faith office.

The order says that religious organizations receiving federal funds must conduct explicitly religious activities in a time and place that are different from when and where they do government-financed work.

But the order also states that faith-based organizations receiving federal dollars may use their facilities to provide government-backed social services, even if those facilities include religious art, icons, scriptures and other religious symbols.

A religious group receiving federal money may also keep religious language in its name, select board members on a religious basis, and include religious references in its mission statements and other documents, the executive order says.

The White House framed the order as an attempt to separate religion from politics, saying in a news release that "decisions about financial awards must be free from political interference or even the appearance of such interference."

But a group that advocates strict church-state separation said the order did not go nearly far enough in that regard.

"I'm disappointed," said the Rev. Barry W. Lynn, executive director of Americans United for the Separation of Church and State. "This leaves much of George W. Bush's faith-based initiative in place. That's not the change many Americans hoped for when President Obama took office."

"I am particularly frustrated that President Obama still has done nothing to ban hiring bias by publicly funded religious charities," Lynn said in a statement. "That's the 800-pound gorilla in the room. No American should be denied a government-funded job because he or she holds the 'wrong' views about religion."

At the same time, Americans United applauded the order for requiring federal agencies to provide alternatives for people who do not want to receive social services at religious charities and praised a new requirement that faith groups receiving federal money be listed on government websites.

The White House faith office was launched by President George W. Bush in 2001 and was retained by Obama, to the disappointment of some church-state separation advocates. Obama tweaked the name of the office, calling it the White House Office of Faith-Based and Neighborhood Partnerships.

While the Bush office was aimed mostly at helping to "level the playing field" for faith-based and nonprofit groups applying for federal money to tackle problems like poverty and substance abuse, Obama's faith office has focused on non-financial relationships with faith and nonprofit groups.

The office has come under fire from Bush administration officials, who say the White House is abusing it for political gain.

Responding to charges from those officials that a conference call Obama hosted with religious leaders on the new health care law crossed the line into political outreach, the White House said last month that "there could hardly be a more appropriate audience" for such a call.

"When congregants fall ill, faith communities come together to support their brothers and sisters in need," Joshua DuBois, executive director of the White House Office of Faith-Based and Neighborhood Partnerships, wrote on the White House blog.

The White House response came after former Bush aides publicly criticized the conference call, saying it was an example of Obama abusing the office to win political support from religious leaders.

"According to the White House website, the faith-based office exists 'to more effectively serve Americans in need,'" Jim Towey, who directed Bush's faith office, wrote in a Wall Street Journal op-ed in September. "I guess that now means Americans in need of Democratic talking points on health care."