"President-elect Obama has again demonstrated his genuine commitment to bringing all Americans of goodwill together in search of common ground," Warren said in a statement. "I applaud his desire to be the president of every citizen."
Warren, in recent weeks, has been barraged with criticism from gay rights advocates because of his support for the anti-gay marriage measure Proposition 8 and for comparing same-sex marriage with incest and pedophilia in an interview, although he later clarified that he doesn't believe gay partnerships are the same as the other two sexual behaviors.
Critics have called Obama to rescind his invitation to Warren, accusing the evangelical pastor of being a "homophobe." They also argue that the invitation contradicts Obama's promise to support greater gay and abortion rights.
Obama has, however, defended his selection of Warren saying that the inauguration will feature "a wide range of viewpoints" and one of the trademarks of America is its diversity.
Robinson was among the critics, calling the Warren invitation a "slap in the face," according to The Washington Post.
In 2003, Robinson became the first openly gay clergy to be elected bishop in The Episcopal Church. His appointment as bishop, among other issues, has sparked severe division in the Anglican Communion with conservative Episcopal churches and dioceses splitting off from the denomination.
The controversial bishop will give the prayer on the first day of formal inaugural events in Washington this Sunday.
In preparation for the event, the bishop said he has read inaugural prayers throughout history and was "horrified" at how "specifically and aggressively Christian they were," according to the New York Times.
For his prayer, Robinson said he is "very clear" that it "will not be a Christian prayer, and I won't be quoting Scriptures or anything like that."
"The texts that I hold as sacred are not sacred texts for all Americans, and I want all people to feel that this is their prayer," he said.
Robinson said he might make the prayer out to "the God of our many understandings."
He also said his partner of more than 20 years, Mark Andrew, would accept an invitation from the Obama team to join him in several inaugural events, according to the NY Times. The two had a civil union ceremony last summer in a New Hampshire church.