(CNN) -- Prominent liberal groups and gay rights proponents criticized President-elect Barack Obama Wednesday for choosing evangelical pastor Rick Warren to deliver the invocation at the presidential inauguration next month.

President-elect Barack Obama has chosen pastor Rick Warren to deliver the invocation at his inauguration.

Warren, one of the most influential religious leaders in the nation, has championed issues such as a reduction of global poverty, human rights abuses and the AIDS epidemic.

But the founder of the Saddleback Church in Lake Forest, California, has also adhered to socially conservative stances -- including his opposition to gay marriage and abortion rights that puts him at odds with many in the Democratic Party, especially the party's most liberal wing.

"[It's] shrewd politics, but if anyone is under any illusion that Obama is interested in advancing gay equality, they should probably sober up now," Andrew Sullivan wrote on the Atlantic Web site Wednesday.

People for the American Way President Kathryn Kolbert told CNN she is "deeply disappointed" with the choice of Warren and said the powerful platform at the inauguration should instead have been given to someone who has "consistent mainstream American values." iReport.com: What do you think of the pick?

"There is no substantive difference between Rick Warren and James Dobson," Kolbert said. "The only difference is tone. His tone is moderate, but his ideas are radical."

Dobson, a social conservative leader, is founder and chairman of Focus on the Family.

Linda Douglass, a spokeswoman for Obama, defended the choice of Warren, saying, "This is going to be the most inclusive, open, accessible inauguration in American history."

"The president-elect certainly disagrees with him on [lesbian, gay, bisexual, transgender] issues," Douglass said. "But it has always been his goal to find common ground with people with whom you may disagree on some issues."

Douglass also noted that Obama and Warren agree on several issues, including advocating on behalf of the poor, the disadvantaged and people who suffer from HIV/AIDS. Watch CNN's Anderson Cooper and his panel discuss the selection »

Warren's support of California's Proposition 8, a measure that outlaws same-sex marriage in the state, sparked the ire of many gay rights proponents earlier this fall.

Warren, who has made it a practice not to endorse candidates or political parties, wrote in October that the issue of gay marriage is not a political issue, but instead "a moral issue that God has spoken clearly about."

"For 5,000 years, every culture and every religion -- not just Christianity -- has defined marriage as a contract between men and women," Warren wrote in a newsletter to his congregation. "There is no reason to change the universal, historical definition of marriage to appease 2 percent of our population."

Warren also stirred controversy earlier this week when he told Beliefnet.com his grounds for opposing same-sex marriage lay primarily on his right of free speech.

"There were all kinds of threats that if [Proposition 8] did not pass, then any pastor could be considered doing hate speech if he shared his views that he didn't think homosexuality was the most natural way for relationships, and that would be hate speech."

Joe Solmonese, president of the Human Rights campaign, said Wednesday he feels a "deep level of disrespect" over the choice of Warren and is calling on Obama to reconsider the move.

"By inviting Rick Warren to your inauguration, you have tarnished the view that gay, lesbian, bisexual and transgender Americans have a place at your table," Solmonese said in an open letter to Obama that was released by his organization.

In his recent interview with Beliefnet, Warren also sparked outrage among supporters of abortion rights for criticizing those who have said abortion would be "safe and rare."

"Don't tell me it should be rare," he said in the interview. "That's like saying on the Holocaust, 'Well, maybe we could save 20 percent of the Jewish people in Poland and Germany and get them out and we should be satisfied with that -- I'm not satisfied with that. I want the Holocaust ended."

But Warren, whose church attracts more than 20,000 people a week, has widely been recognized for his attempts to expand the evangelical movement beyond socially conservative issues.

In the 2008 election, Warren hosted Obama and Sen. John McCain, the Republican presidential nominee, at a candidate forum held in his church.

His book "The Purpose Driven Life" has sold more than 20 million copies since it was first published five years ago, and Time magazine named him one of the 25 most influential evangelicals in 2005.

"Many believe that Warren ... is the successor to the [Rev. Billy Graham] for the role of America's minister," Time wrote in 2005.

CNN's Rebecca Sinderbrand contributed to this report

All About Barack Obama • Rick Warren • U.S. Presidential Inauguration • Same-Sex Marriage