DENVER — The nation’s rapidly growing Latino population is one of the most powerful forces working in President Barack Obama’s favor in many of the states that will determine his contest with Mitt Romney. But Latinos are not registering or voting in numbers that fully reflect their potential strength, leaving Hispanic leaders frustrated and Democrats worried as they increase efforts to rally Latino support.

Interviews with Latino voters across the country suggested a range of reasons for what has become, over a decade, an entrenched pattern of nonparticipation, ranging from a distrust of government to a fear of what many see as an intimidating effort by law enforcement and political leaders to crack down on immigrants, legal or not.

Here in Denver, Ben Monterosso, the executive director of Mi Familia Vota, or My Family Votes, a national group that helps Latinos become citizens and register to vote, gathered organizers around a table in his office and recited census data demonstrating the lack of Latino participation.

“Our potential at the ballot box is not being maximized,” Monterosso told them. “The untapped potential is there.”

More than 21 million Latinos will be eligible to vote this November, clustered in pockets from Colorado to Florida, as well as in less obvious states such as Illinois, Iowa, North Carolina and Virginia. Yet just over 10 million of them are registered, and even fewer turn out to vote.

In the 2008 presidential election, when a record 10 million Latinos showed up at the polls nationwide, that amounted to just half of the eligible voters. By contrast, 66 percent of eligible whites and 65 percent of eligible blacks voted, according to a study by the Pew Hispanic Center.

That disparity is echoed in swing states across the country. In Nevada, 42 percent of eligible Latinos are registered, while just 35 percent are registered in Virginia, according to Latino Decisions, a political research organization that studies Latino voting trends.

Although Latinos do not turn up at the polls in the same numbers, relative to their population, as other ethnic groups, their overall numbers are growing so rapidly that they are nevertheless on the verge of becoming the powerful force in U.S. politics that officials in both parties have long anticipated — an effect that would only be magnified should they somehow begin to match the voting percentages of other ethnic groups.

Obama’s campaign has seized on that as a central part of his re-election strategy, with an early burst of three Spanish-language TV ads in four swing states, including Colorado, and voter registration drives in Latino neighborhoods.

“Hi, are you registered to vote?” Linda Vargas, 62, said in English and Spanish to people walking into a public library on the outskirts of Denver as she sat behind a table stacked with voter registration forms.

This segment of the U.S. electorate is by any measure sprawling, with near-explosive population growth in places like California and Texas and growing numbers in swing states like Arizona, Colorado, Florida, Nevada and New Mexico. Their presence in such politically important states has only fed the frustration of Latino organizers over their underrepresentation at the polls.

Matt Barreto, an associate professor of political science at the University of Washington and head of Latino Decisions, said the population growth had produced a higher Latino vote in every presidential election over the past decade, a number that had the effect of masking the political apathy of many Latino voters.

Jim Messina, Obama’s campaign manager, said Latino voters were a critical factor in the president’s re-election hopes. “Look, if we do our job right and have a good ground game, I absolutely believe that Latino voters can be one of the big reasons we win this election,” he said.

Officials in Romney’s campaign argued that he would cut into Obama’s Latino support by challenging his record on the economy, and how, they said, it had been harmful to Latinos.

Last week, the Romney campaign posted a Spanish-language advertisement on its website pointing to rising unemployment among Latinos.

“Understand the dynamic of this election: It’s about the economy and it’s about jobs,” said Joshua Baca, Romney’s coalitions director, who is responsible for outreach efforts to Hispanics. “Whatever the Obama campaign wants to do with regards to targeting Hispanic voters, that’s fine. Our message is going to be, ‘It doesn’t matter if you are Hispanic, if you’re a woman, if you’re African-American: It’s the economy.'”

Latino voters overwhelmingly support Obama over Romney, according to recent polls. The anger at Republicans for supporting tough immigration laws, like the one passed in Arizona last year, is powerful and potentially damaging to Romney after a Republican primary in which the candidates largely rallied behind that law.