WASHINGTON — With immigration legislation stalled in Congress, Hispanics and Asian-Americans say getting relief from deportations is more important for many of the 11 million immigrants here illegally than creating a pathway to U.S. citizenship, a new study finds.

Two polls released today by the Pew Research Center expose a potential conflict for two minority groups that voted overwhelmingly last year for President Barack Obama, a Democrat. Obama is under pressure from immigration supporters to use his executive power to stop deportations.

Strong majorities of both Hispanics and Asian-Americans continue to back a pathway to citizenship, 89 percent and 72 percent, respectively. Still, by 55 percent to 35 percent, Hispanics said being able to live and work in the U.S. legally without the threat of deportation was more important. Among Asian-Americans, the ratio was 49 to 44 percent.

Among both groups, noncitizens are more apt than citizens to consider it important to remove the threat of deportation.

Not all Latino immigrants in the U.S. seek to become American citizens, according to the Pew study. Of Hispanic immigrants who came to the U.S. legally, just 44 percent have become citizens, due in part to the cost of applying as well as worries about passing the English part of the citizenship test. Among immigrants from Mexico, the largest country of origin, the share is even lower, at 36 percent.

“There’s no question that these groups want a pathway to citizenship for the unauthorized, but the surveys also show that, especially for Latinos, it’s the threat of deportation that casts the longest shadow on their communities,” said Mark Hugo Lopez, Pew’s director of Hispanic research and report author.

Earlier this year, the Senate passed legislation that would strengthen border enforcement and allow a 13-year pathway to citizenship. But activity has stalled in the GOP-controlled House, with the citizenship provision a major sticking point.