Still, Gallup noted that John F. Kennedy won the presidency in 1960 despite the 21 percent of Americans who said they would not vote for a Catholic president.
Separate Gallup polls show the former Massachusetts governor essentially tied with President Barack Obama.
This year, nearly 8 in 10 Catholics, Protestants and religiously unaffiliated Americans said they would vote for a qualified Mormon candidate, with little statistical difference between the groups.
Rather, anti-Mormon bias is closely tied to education levels and partisanship, Gallup said.
Nearly a quarter of Americans with a high school education or less said they would not vote for a Mormon; that number decreases to just 7 percent among those with postgraduate degrees.
Nine in 10 Republicans and 79 percent of independents said they would vote for a Mormon; just 72 percent of Democrats agreed.
Gallup began asking the Mormon question in 1967 when former Michigan Gov. George Romney, Mitt Romney's father, was a top candidate for the GOP nomination. That year, 19 percent said they would not vote for a Mormon presidential candidate.
This year, 18 percent said they would not vote for a qualified Mormon candidate, down from 22 percent in 2011.
A Salt Lake Tribune national poll late last year showed that 26 percent of U.S. voters were either "very" or "somewhat" uncomfortable voting for a Mormon for president.
Among Republicans, 14 percent were uncomfortable with the prospect of an LDS commander in chief, compared with 27 percent of independents and 36 percent of Democrats, according to The Tribune survey.
The anti-Mormon bias remains remarkably consistent, according to Gallup, considering that resistance to candidates who are black, Jewish or a woman has declined markedly since 1967.
Anti-Mormon sentiment tends to rise slightly when when Latter-day Saints are running for president, Gallup noted, with the all-time high of 24 percent coming during Romney's first presidential campaign in 2007.
The Gallup poll is based on telephone interviews conducted June 7-10 with a random sample of 1,004 adults. The poll has a margin of error of plus or minus 4 percentage points.