Dozens of well-wishers made the pilgrimage Sunday to The Carter Center in Atlanta, as prayers and memories of President Carter’s legacy were offered up at his small Baptist church in Plains, Georgia, a day after he entered hospice care.

Among those paying homage was his niece, who noted the 39th president’s years of service in an emotional address at Maranatha Baptist Church, where Carter taught Sunday school for decades.

“I just want to read one of Uncle Jimmy’s quotes,” Kim Fuller said during the Sunday school morning service, adding: “Oh, this is going to be really hard.”

She referenced this quote from Mr. Carter: “I have one life and one chance to make it count for something. I’m free to choose that something. … My faith demands that I do whatever I can, wherever I can, whenever I can, for as long as I can.”

“Maybe if we think about it, maybe it’s time to pass the baton,” Ms. Fuller said before leading those gathered in prayer. “Who picks it up, I have no clue. I don’t know. Because this baton’s going to be a really big one.”

Mr. Carter, at age 98 the longest-lived American president, had a recent series of short hospital stays. The Carter Center said in a statement Saturday that the 39th president has now “decided to spend his remaining time at home with his family and receive hospice care instead of additional medical intervention.”

In Atlanta, people, some traveling many miles, made the trip to the Carter Center to reflect on the life of the former president on a spring-like Sunday under a sunny sky.

“I brought my sons down here today to pay respect for President Carter and teach them a little bit about how great a humanitarian he was, especially in the later stages of his life,” said James Culbertson, who drove an hour to Atlanta from Calhoun, Georgia.

The presidential library itself was closed in honor of President’s Day weekend, but people were still showing up to walk past the fountains and through the gardens.

David Brummett of Frederick County, Maryland, said he changed his Sunday morning plans when he heard news that Mr. Carter was in hospice care.

Mr. Brummett paused near a large statue of Mr. Carter, where someone had placed some violets at the base.

“Great man, great president, probably under-appreciated by those who didn’t know much about him,” Mr. Brummett said. “People should come here to appreciate the life, and the contributions he made both during his presidency and after.”

Following Ms. Fuller’s Sunday school service at Maranatha Baptist Church, Pastor Hugh Deloach offered prayers for the Carter family, particularly for Rosalynn Carter, the wife of the former president.

The Carters have been married for more than 75 years, making American history as the longest-married presidential couple.

“Lord, especially Mrs. Carter, and God look back on times and years that they’ve been together and Lord just strengthen her in the power of your might as well,” the pastor said.

Others took to social media to remember Mr. Carter, who served one term after defeating President Gerald Ford in 1976.

“Across life’s seasons, President Jimmy Carter, a man of great faith, has walked with God. In this tender time of transitioning, God is surely walking with him,” Senator Warnock, a Georgia Democrat, said in a tweet.

“May he, Rosalynn & the entire Carter family be comforted with that peace and surrounded by our love & prayers.”

The Carters volunteered for decades with Habitat for Humanity, beginning in 1984 and continuing until 2020.

“All of us at Habitat for Humanity are lifting up President and Mrs. Carter in prayer as he enters hospice care,” Habitat for Humanity International CEO Jonathan Reckford said in a statement.

“We pray for his comfort and for their peace, and that the Carter family experiences the joy of their relationships with each other and with God in this time,” Mr. Reckford said.

Nicholas Kristof, a New York Times columnist, tweeted: “Prize winners and truly impressive people. Few are as truly good as Jimmy Carter, who at age 98 is now entering hospice. He leaves this planet so much better than he found it. A great, great, great man.”

Mr. Carter was a little-known Georgia governor when he began his bid for the presidency ahead of the 1976 election. He went on to defeat Mr. Ford, capitalizing as a Washington outsider in the wake of the Vietnam War and the Watergate scandal that drove Richard Nixon from office in 1974.

Mr. Carter served a single, tumultuous term and was defeated by Republican Ronald Reagan in 1980, a landslide loss that ultimately paved the way for his decades of global advocacy for democracy, public health and human rights via The Carter Center.

The former president and his wife, Rosalynn, 95, opened the center in 1982. His work there garnered a Nobel Peace Prize in 2002.