Albuquerque, New Mexico (CNN) -- An event billed as a discussion on the economy turned personal Tuesday when a woman asked President Barack Obama about his Christian faith and views on abortion.

The question came at a town hall-style meeting in the yard of an Albuquerque home as part of Obama's public outreach to explain his policies and campaign for Democrats in the November congressional elections.

With a recent survey showing that only a third of Americans can correctly identify Obama as a Christian, the president gave a personal account of his conversion as an adult and how his public service is part of his faith.

"I am a Christian by choice," Obama began, standing beneath a blazing sun, when asked why he is a Christian.

"I came to my Christian faith later in life, and it was because the precepts of Jesus Christ spoke to me in terms of the kind of life that I would want to lead," Obama said. "Being my brothers' and sisters' keeper. Treating others as they would treat me. And I think also understanding that, you know, that Jesus Christ dying for my sins spoke to the humility that we all have to have as human beings."

Humans are "sinful" and "flawed" beings that make mistakes and "achieve salvation through the grace of God," the president continued, adding that we also can "see God in other people and do our best to help them find their, you know, their own grace."

"So that's what I strive to do," Obama said. "That's what I pray to do everyday. I think my public service is part of that effort to express my Christian faith."

At the same time, Obama emphasized his belief that freedom of religion is "part of the bedrock strength" of the United States.

"This is a country that is still predominantly Christian, but we have Jews, Muslims, Hindus, atheists, agnostics, Buddhists" and others, he said, adding that "their own path to grace is one that we have to revere and respect as much as our own, and that is part of what makes this country what it is."

The same questioner also asked Obama about regulations on early and late-term abortion, a politically charged issue in the abortion debate.

Obama responded that abortion should be "safe, legal and rare" in America, adding that families -- not the government -- "should be the ones making the decision."

Restrictions against late-term abortion are in place now, he said, adding that "people still argue and disagree about it. That's part of our Democratic tradition."

On September 19, Obama publicly attended church for the first time in nearly six months when the first family joined the 9 a.m. service at St. John's Church Lafayette Square, an Episcopal congregation about a block from the White House.

The family sat a few rows from the altar, among roughly 40 worshippers. Each family member received communion, led by the president.

A survey conducted in late July and early August by the Pew Forum on Religion and Public Life found that nearly one in five Americans believe Obama is a Muslim, up from around one in 10 Americans who said he was Muslim last year.

The number of Americans who expressed uncertainly about the president's religion, meanwhile, is much larger and has also grown, including among Obama's political base. For instance, fewer than half of Democrats and African-Americans now say that Obama is Christian.

According to the Pew survey released last month, most of those who think Obama is Muslim are Republicans, but the number of independents who believe he is Muslim has expanded significantly, from 10 percent last year to 18 percent this summer.

In March 2009, 36 percent of African-Americans said they didn't know what religion Obama practices. Now, 46 percent of African-Americans say they don't know, according to the survey.