By Laurie Goodstein

For more than 50 years, the National Prayer Breakfast has served as a prime networking event in Washington, bringing together the president, members of Congress, foreign diplomats and thousands of religious, business and military leaders for scrambled eggs and supplication.

Usually, the annual event passes with little notice. But this year, an ethics group in Washington has asked President Obama and Congressional leaders to stay away from the breakfast, on Thursday. Religious and gay rights groups have organized competing prayer events in 17 cities, and protesters are picketing in Washington and Boston.

The objections are focused on the sponsor of the breakfast, a secretive evangelical Christian network called The Fellowship, also known as The Family, and accusations that it has ties to legislation in Uganda that calls for the imprisonment and execution of homosexuals.

The Family has always stayed intentionally in the background, according to those who have written about it. In the last year, however, it was identified as the sponsor of a residence on Capitol Hill that has served as a dormitory and meeting place for a cluster of politicians who ran into ethics problems, including Senator John Ensign, Republican of Nevada, and Gov. Mark Sanford, Republican of South Carolina, both of whom have admitted to adultery.

More recently, it became public that the Family also has close ties to the Ugandan politician who has sponsored the proposed anti-gay legislation.

Citizens for Responsibility and Ethics in Washington, a government watchdog group, sent a letter this week to the president and Congressional leaders urging them to skip the prayer breakfast. They have also called on C-Span not to televise it this year.

Melanie Sloan, executive director of the ethics group, said: “It is a combination of the intolerance of the organization’ views, and the secrecy surrounding the organization. It doesn’t mean they shouldn’t be allowed to hold their breakfast; of course they should. The question is, Should American officials be lending legitimacy to it, giving their imprimatur by showing up.”

The Family has no identifiable Internet site, no office number and no official spokesman. J. Robert Hunter, a member who has spoken publicly about the group, said that it was unfair to blame the Family for the anti-gay legislation introduced by David Bahati. Mr. Hunter said that about 30 Family members, all Americans, active in Africa recently conveyed their dismay about the legislation to Ugandan politicians, including Mr. Bahati.

Mr. Hunter said the recent controversies had prompted a debate within the group about its lack of transparency. “I and quite a few others are saying we should be much more open,” he said.

Jeff Sharlet, author of “The Family: The Secret Fundamentalism at the Heart of American Power” (Harper Perennial, 2009) said in a telephone interview, “Here’ an organization that, in the past, has not acknowledged its own existence.”

“It’ not a sinister plot. This is their theological stance,” said Mr. Sharlet, who infiltrated the group to do research for his book. “Their leader, Doug Coe, says that the more invisible you can make your organization, the more influence it will have.”

A White House official said that Mr. Obama, like each president since Dwight D. Eisenhower, planned to attend the breakfast. Michelle Obama, Secretary of State Hillary Rodham Clinton, and other cabinet members will also attend. The president will deliver remarks about “the importance of an openness to compromise,” the official said.

The official also said that the president and the State Department had spoken out strongly against the legislation in Uganda.

The breakfast, which usually features a prominent keynote speaker (past ones have included Bono, Mother Teresa and former Prime Minister Tony Blair of Britain), is only the most visible in several days of gatherings where the Family’ networking takes place in smaller groups. There are separate meetings for African politicians, military leaders, business people and media professionals, to name a few.

Many states also have prayer breakfasts this week, which may appear to be government-sponsored but are also mostly affiliated with the Family.

Liberal members of the clergy and gay rights leaders organized the alternative events in haste this year, calling theirs the American Prayer Hour. The will convene at places like Calvary Baptist Church in Washington; Glendale City Seventh-day Adventist Church in California; the bishop’ chapel of the Episcopal Diocese of Western New York, in Rochester; and Covenant Community Church in Center Point, Ala.

Wayne Besen, executive director of Truth Wins Out, a gay rights group, said he initiated the prayer-hour idea because many religious Americans who attend the breakfasts have no idea about the connection to the Family and the anti-gay legislation.

“They have symbolically taken the mantle of religion,” Mr. Besen said, “and I think it’ time to take it back. And the American Prayer Hour is a step in that direction.”